The situation with the crown dependencies is complex but not it doesn’t have to be confusing.
The Isle of Man and Channel Islands are feudal possessions of the crown. They are different from the United Kingdom which is a country of which the Queen is monarch, but the United Kingdom isn’t a “possession” of the Queen. She’s sovereign, but not a feudal lord (even though her titles are feudal in origin.)
The Lord of Man is an ancient feudal title, referring to the feudal ruler of the island. That holder of that title became a vassal of the English monarch in 1399, and remained so permanently after (previous Lords of Man had been vassals of both the Kings of Scotland and England, at various times.)
In the 1700s the 2nd Duke of Atholl, also the hereditary Lord of Man, sold the title Lord of Man to the Kingdom of Great Britain for £70,000.
To understand what next, you must understand what the United Kingdom actually is and some basics of government systems from 300-500 years ago. Before 1707, there was a legitimate “Kingdom of Scotland” and a “Kingdom of England.” Wales was part of the Kingdom of England, while Wales had been an independent realm long ago, the English Kings had long since formally eradicated it as a separate legal entity and made it part of the Kingdom of England. It’s only in more modern times you’ve seen devolution of significant rights and separate powers to Wales.
Everyone knows Queen Elizabeth I, but what many for some reason forget is her death was quite possibly more important than her life–because it unified the monarchies of Scotland and England. Elizabeth never married and had no heir, so someone not her direct lineal descendant of course had to inherit her. It ended up under the family tree the next closest line heir was James, reigning King of Scotland. When Elizabeth died he became James I of England (he was James VI of Scotland.) James essentially immediately went to England, and it being the far more impressive realm he appeared to all but forget the country in which he was born and never returned (later monarchs have more deliberately made sure to spend time in Scotland to appease the locals.)
During the life of James I and for some time after, England and Scotland were in what is called a “dual monarchy.” This wasn’t at all uncommon in medieval to late medieval to renaissance Europe. The royal families intermarried, a lot. So it wasn’t at all uncommon per se for a King of one country to inherit the crown of another. But usually the two countries retained distinct legal systems, governments, and even laws of succession. This is why not only were Kingdoms unified under one ruler by inheritance, but dual monarchies could and frequently did split back up, when the heir of one crown would end up being different from the crown of the other (which happened because most countries of Europe had similar, but sightly different, laws of succession.)
In 1707, the Acts of Union did away with the dual monarchy. That is why anytime someone refers to the "Queen of England’ a know-it-all is quick to interject “there’s no such thing!” And, they’re correct. The country of England does have a monarch, but only in the sense that England is part of the United Kingdom, which has a monarch. Queen Elizabeth isn’t the Queen of Scotland or England or Wales or Northern Ireland, she’s the Queen of the United Kingdom. Now, in 1707 Queen Anne became “Queen of Great Britain” the Kingdom of Great Britain, by act of parliament in 1800, merged with the Kingdom of Ireland and became the “United Kingdom of Great Britain and Ireland”, which is the same country we have today, although it has renamed itself the United Kingdom of Great Britain and Northern Ireland due to the independence of the Republic of Ireland.
Without such a legal act, separate possessions of the crown do not “merge” into the country proper. So, quite simply, because the Kingdom of Great Britain bought the “title” of Lord of Man, but never incorporated man into the United Kingdom, it simply never became part of it.
What does that mean legally? In theory at one point in time the Lord of Man could act as a tyrant. In practice, the Isle of Man’s feudal leader has been hands off for a long while–even before the 2nd Duke of Atholl sold the title to the crown, instead the Isle of Man has been lead by a type of legislative body for ages–they in fact make claim to having one of the oldest legislatures in the world. [They fight with San Marino, Iceland, and a few other places for this claim, and there is no clear answer as to which is really oldest.]
A single monarch having possessions with different laws, thus isn’t really that unique. But it becomes a problem as societies move closer to modern times, and the need for democracy and etc is more obvious. So while the government of the United Kingdom doesn’t technically have any legal authority over the Isle of Man (Queen Elizabeth II does), Parliament handles her majesty’s duties as Lord of Man (not Lady) for her, because she is a constitutional monarch. What this has meant as a matter of practicality is the British government extends a citizenship to Manx people, and it “guarantees their good governance and defense”, which basically just means unless things go real bad there they leave them the fuck alone. The Isle of Man consequently is essentially an independent country domestically. They could have had greater union with Britain, but they’ve never wanted it, and are in fact pretty happy not having it.
The Isle of Man is a relict in many ways, it’s the last “remnant” Viking kingdom in the British Isles, and its culture and laws were never really intertwined with that of Great Britain’s.
The Channel Islands have a different history, but it’s similar. They aren’t part of the United Kingdom for essentially the same reason–they are a feudal possession of Queen Elizabeth’s, and those possessions were never by Act of Parliament “incorporated into” the United Kingdom (just as the Isle of Man was not.) The Channel Islands came under the crown in a different way–all the way back to William the Conqueror. Who, as you may recall, was Duke of Normandy. The Channel Islands are the last remnants of the English possession of the Duchy of Normandy. Over hundreds of years English France grew and shrank, until finally it was only a small bit of land around Calais in Normandy–and then finally it wasn’t even that, but the French were never able to get the channel islands, and probably after a point never cared to due to the relative worthlessness in most ways.
Just like Isle of Man they have their own governments, and are essentially independent domestically with British citizenship and Britain being responsible for their “ultimate good governance” and defense.
What’s worth noting is that while neither the Channel Islands or the Isle of Man joined the EU (and did not wish to do so), they are subject to some European organizations–like the European Court of Human Rights. This became relevant in the Isle of Man, because the Manx practiced legal corporal punishment in their legal system (a form of caning) until the latter half of the 20th century), it was only stopped because of the ECHR.
On the Channel Islands, one of the islands (Sark), was subject to a genuinely feudal system, with the Lord of Sark (Seigneur) having essentially true feudal power over the island. He customarily devolved some of it to a council, but he still collected special feudal taxes personally on various things, and exercised genuine power. The people of Sark didn’t seem to mind this situation, but two billionaire brothers (the Barclays) bought an island that was part of the fief of Sark, and chafed at being subject to this minor noble’s rules and his property taxation rights. They worked to change the government on Sark for years, maintaining it wasn’t consistent with the European Convention on Human Rights and waged a lot of litigation. The people of Sark eventually agreed to a new constitution to appease them (they were the wealthiest people on the island and were making investments in the local economy), but there have been complaints that since the 2008 removal of the old feudal system of government it’s been replaced by an undemocratic system of government in which the Barclay brothers have undue influence.
As far as the EU goes–when Britain joined on they had a problem because of these special-status dependencies. These dependencies didn’t want to join the EU, and while in theory Parliament could “force it on them” acting for the Queen (who as a feudal lord legally could actually overrule anything the governments of these possessions legislated) the British deeply respected the historical arrangement. They obtained a special dispensation. Residents of these dependencies would be British citizens but not EU citizens, they would not have most of the immediate benefits of EU citizenship and they would be given special passports denoting this. They also wouldn’t, of course, be subject to EU rules and regulations or anything else. However, if they move to British territory and reside for 5 years, they then become full British/EU citizens, and can get passports indicating such.
So for the Channel Islands and the Isle of Man, leaving the EU will be a lot less meaningful–they were never part of it, and it only really affected them in that they could eventually become part of it. It’s theorized that the EU might “go after” these places, because right now they actually function as tax havens (especially the Isle of Man) because they have easy access to EU markets but are outside the EU itself, a position only tolerated because of the special dispensation given to Britain. If Britain is outside the EU, it’s likely the EU may put in place restrictions designed to prevent some of the international finance shenanigans that go on.