What a particular jurisdiction calls any given crime is just variants in word usage and is often based off archaic language, there’s not a universal standard, so talking about what the exact words requires either generalizing or looking at a specific location’s laws. Larceny was originally a common law crime in the UK, and has since been abandoned there in favor of specific crimes (theft, fraud, robbery). For the most part, larceny is a general term for ‘taking someone else’s stuff with intent to keep it permanently’ and theft is ‘larceny without other stuff tacked on’, and they probably mean the same general thing when you come across them. Theft/larceny is distinct from robbery, ‘taking someone else’s stuff using force or threat of force with intent to keep it’, burglary ‘taking someone else’s stuff by breaking into their property with intent to keep it’ or fraud ‘taking someone else’s stuff using deception with intent to keep it’. The ‘intent to keep it’ distinguishes theft or larceny from crimes like joyriding or trespass, where you take something that’s not yours but the intent is to just keep it temporarily and give it back when you’re done.
Grand vs ‘unmodified’ or ‘petty’ theft/larceny/fraud/robbery/etc. is usually the distinction between a felony or midemeanor. Typically the difference is set out by a dollar value in a statute, and sometimes depends on the nature of goods stolen - stealing a firearm might automatically be grand theft regardless of its value, while stealing medicine might have a lower dollar amount to become grand than general goods. Since vehicles are fairly distinct from other types of property, they are often called out in laws around stealing.
The term “Grand theft auto” was popularized by the game doesn’t actually appear in California’s penal code AFAIK, but is a shorthand used by CA police and for brevity in CA court records. Various cities, states, counties, police forces, etc. will have different things that they use as shorthand, and what they use depends on practical factors. Stealing cars requires a different police response than stealing other items and is a fairly common crime, while stealing filing cabinets is not that common and doesn’t require special handling so there’s no reason to use a phrase like “Grand Theft Filing Cabinet”, it would likely be just something like “Grand theft”
Fraud is generally a crime, and usually follows a similar dollar value distinction to theft or larceny. Small claims court is not a criminal court, small claims court is solely for civil cases that involve a small dollar amount, and the amount will vary from case to case. In most cases involving stealing, the state will pursue a criminal case charging the person with the crime of theft, and the victim will pursue a civil case seeking compensation for the stolen property. They are two separate but related legal actions. That is, if you defrauded me for $500 you might be guilty of the crime of ‘petty fraud’ and the DA would charge that as a crime, seeking to put you in jail, while I would have a civil action to recover the $500 plus any additional damages, which would probably be small enough to happen in small claims court.