Specifically Article 3 Section 2
The judicial power shall extend to all cases, in law and equity, arising under this Constitution,
Looking it up, I am not clear if “equity” refers to civil law (as opposed to criminal law) or common law (as opposed to statutory law).
Equity is a term from British legal tradition that is neither criminal law nor civil common law.
Note that in current US practice, equity and common law have merged
Post-Revolution saw the abolishment of chancery courts in American states such as Massachusetts, New York, and Virginia.[56] This was the result of equity being disfavoured and rejected, until late in the 19th century federal judges revived the equitable injunction.[56] The early amendments of the United States Constitution explicitly acknowledged common law and equity as being clear divisions of jurisprudence. However, Rule 2 of the Federal Rules of Civil Procedure came into effect in 1938 to unite common law with equitable claims.[57]
The fictional case “Jarndyce vs Jarndyce” from Dickens, was an inheritance case in equity - which was taken from examples of real cases that lasted for many decades.
More useful link
In modern legal practice, the two are separated by the way in which the cases are heard and the type of decision that can be handed down. Most cases in common law are heard by a jury, with a judge as arbiter, and decisions can result in punishment or financial restitution.
Equity cases, however, are typically heard only by a judge who passes judgment on the case, which can take the form of action or cessation of action by one party. Someone who steals a computer, for example, might be ordered by a common law court to repay the value of the computer to the wronged party, which would be just but may not be fair. A court of equity, on the other hand, could order the computer be returned to the owner as a more equitable solution to the situation.
It’s a separate branch of law that deals with things such as trusts. For historical reasons, English law used to be divided between “law” in the narrow sense and equity, even though both were (and are) legal systems based on precedent, and lawyers were (and are) expected to know both. Until the 1870s they were administered in separate courts in England. America never had separate courts for law and equity - they have always been administered in the same courts. The distinction does therefore not matter much in American law, but English law still likes to draw the line at least terminologically.
Which is why you can sue in civil court for equitable relief. For example, if you are suing to enforce a contract, you would sue for a legal remedy for breach. But you would also likely include a count based on some equitable theory (like promissory estoppel) which argues that, even if the court decides that there is no contract, you should still be entitled to some sort of compensation as a matter of fairness.
As another example, it’s equity that allows you to seek an injunction- force somebody to stop doing something, such as harass you, or demolish some prized building.
Thanks!
Little bit of nitpicking - there isn’t a single concept of “British law” for the purposes of this discussion.
The equitable principles that are being discussed here come from English law.
Scotland has a different legal system, derived from Dutch-Roman law, which is historically separate from the English (and Welsh) common law.
Scots law does have a concept of equity, but it was never developed as a separate area of the law and doesn’t have the same sharp division from other principles of Scots law, unlike the sharp division which English equity historically had from the common law.
D’oh. Normally, when I’m tempted to write “English” I mean “British” - butI overcorrected here
And another bit of nitpicking - yes, the Brits did bring courts of equity with them to the colonies, both in what became the US, and in British North America. The Americans in particular developed a suspicion of equity courts, because there were no juries in courts of equity, and because the governor was often a member of the chancery courts, if not the only judge.
One of the best known courts of chancery was in New York, where the Chancellor was the highest ranking judge in the state court system. It continued as a separate court until its abolition in 1847.
Chancellor Kent of New York was one of the earliest major exponents of American law, and his commentaries became highly regarded.
According to LII, courts in Delaware, Mississippi, Tennessee and New Jersey continue to be courts of equity. The Delaware Court of Chancery is heavily involved in corporations law, which is a specialty of Delaware law.
Ontario and the Atlantic provinces of Canada also had chancery courts, but they were gradually merged with the common law courts.
As far as I know, Quebec never had a chancery court, because equity as a separate area of law is foreign to the civil law.
And the four western provinces established their court systems after the English merger of law and equity, so I don’t think they ever had an equity court. In BC, the governor may have had an equitable jurisdiction, but I don’t know for sure. If so, didn’t survive as a separate court.
(And now @Schnitte is wondering why he came back to the SDMB to be nitpicked… 
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Equity endeavours to be ‘fair’ to all the parties in the case, rather than just refining a single point for consideration by a jury. Chancery court, in the English system, developed a notorious reputation for delay, partly because the court was overstretched and under-resourced for the amount of work that it had.
It happens. 
I remember reading an equity textbook years ago whose author said, in the preface, that in his university lectures he’d often ask students what they think equity is. The answer he usually gets is that it is a branch of the law concerned with fair and just outcomes to a case. When he gets an answer like this, he’d then ask the student the counter question: So this means that the law, as opposed to equity, is concerned with unfair and unjust outcomes?
I find this anecdote quite telling. It is true that, historically, equity developed as a separate body of rules to correct the results of overly rigid and formalistic rules in the common law. But this is history. As things stand today, equity is just as much law as “law” (in the narrow sense) is. For practical intend and purposes, it is a weird term for the branch of law that includes trusts, fiduciary duties, and special types of remedies (injunctions, specific performance) where pecuniary damages would be inadequate.
The Delaware Court of Chancery was briefly in the national news last year, when Twitter sued Elon Musk to proceed with his original purchase offer. The case proceeded through the Delaware Court of Chancery until Musk decided to go through with the purchase after all. And the rest is history.
The common law and equity were once separate legal systems with different conceptual underpinnings.
The common law involved the King of England empowering judges to decide case based on a common, England-wide, set of precedents. The judge would make a decision, by trying to fit the facts of the present case into a framework of principles taken from centuries of previous cases.
Of course, people might be upset with this and would take their cases to the King, who had more flexibility and might more readily rule in their favour.
So the Kings delegated this role as well, to a minister known as the Lord Chancellor. In turn it was delegated again to the Court of Chancery.
The Chancellor / Chancery was in theory not bound by common law precedent. Instead cases were determined by a set of equitable principles that attempted to determine the “fair” outcome. Of course this system became hidebound as well.
So now (the year 1400 or so) you had two sets of courts: common law courts and chancery or equity courts.
Criminal law, contract and tort arose from the common law courts. Trusts and certain remedies arose in the equity courts.
Most systems of law based on English law have now merged the common law and equity courts into a single court system, empowered to take elements from each legal system. So you can sue for breach of contract (originally common law) and seek a remedy of specific performance (other party forced to carry out some contractual obligation, originally an equitable concept).
So to answer the OP’s question, this merger hadn’t happened yet in the 1780s (though it wasn’t far off). The US Constitution’s drafters were trying to make clear that the judges were empowered to hear cases whether they involved matters of “law” (common law) or equity.
Tennessee still has separate courts for law and equity. Sort of.
CIRCUIT COURTS
Circuit Courts are courts of general jurisdiction in Tennessee. Circuit court judges hear civil and criminal cases and appeals of decisions from Juvenile, Municipal, and General Sessions Courts. The jurisdiction of circuit courts often overlaps that of the chancery courts. Criminal cases are tried in circuit court except in districts with separate criminal courts established by the General Assembly.CHANCERY COURTS
Chancery Courts are courts of equity that are based on the English system in which the chancellor acted as the “King’s conscience.” A chancellor, the judge who presides over chancery courts, may modify the application of strict legal rules and adapt relief to the circumstances of individual cases. Chancery Courts handle a variety of issues including lawsuits, contract disputes, application for injunctions and name changes. A number of matters, such as divorces, adoptions, and workers’ compensation, can be heard in either chancery or circuit court.
About the Trial Courts | Tennessee Administrative Office of the Courts (tncourts.gov)
Virginia has a separate chancery court from 1777 until 1831, with exclusively equity jurisdiction.
Virginia also kept law pleading and equity pleading separate (although in the same court) until 2006.
It seems that my (inaccurate) claim that America has never had separate courts for law and equity was based on something I had read years ago about the federal courts. At the federal level, law and equity have always been merged. I inaccurately generalised this to all American courts, including the state level.
Until 2001, Arkansas had separate courts of equity called the Chancery Court. Instead of a judge there was a chancellor. Courts of law were the Circuit Court with a circuit judge and a mishmash of lower courts. Divorces were considered a matter of equity and were always filed in the Chancery Court.
Interestingly, the chancellor and the judge were the same person and the hearings were held in the same court room staffed by the same people.