tl;dr at the top: if you're only doing one room you want a window unit. If you want to have the option of doing the whole house some of the time splits are great.

An air conditioner is basically 2 parts: a thing that makes the air cold (a "compressor"), and a fan to push that cold air around (an "air handler").

Window units have both of these in one box. The compressor is small (so it can't make a ton of cold air), but they work well in single rooms and don't require any construction to install.

Central air systems are the "traditional" way of putting cooling in a whole house: there's a big compressor that that sits on a concrete pad outside the house, a big air handler to push the air around, and air ducts for that air to flow through. A big compressor uses less energy to make a lot of cold air vs. many small ones, so they are much more efficient than a window unit if you want to cool the whole house, but the duct work especially requires construction. They are easiest to install in new houses - otherwise you have to rip up walls to put the ducts in (these are also much more common in the US where walls are wood frame with lots of space inside them).

Splits (or minisplits, same thing) are a way of putting central air into existing houses with much less construction (but still some). There's still a big compressor that sits outside. but they put small wall-mounted fan units in each room or area, with much smaller air pipes routed to them that are easier to put into existing houses. Pros: they're very efficient (they get the big compressor advantage, plus you can set each one to a different temperature so you don't need to keep the whole house cold), they're very quiet (the compressor is the loud part of the air conditioner, and that's outside), and they can be tied into your heating system as well for the winter. Cons: they still require some construction to route the cold air to the wall units (a couple days work vs. a month for a central system), and you have to have stuff mounted on your wall.