So you can already kinda see how the different instances differ.
They all for the most part run the same server which means they will all look the same. The difference then comes down to how they will manage the server and moderate the users.
I can't give specifics between lemm.ee and lemmy.world because I haven't really seen much from the admins. I know Ruud, the admin of lemmy.world, also hosts large instances of other federated platforms like Mastodon, so it can be assumed they are experienced with hosting and there will likely be limited service interruptions that other instances may face.
One instance may be more relaxed with controversial topics and not block them from happening, one may want to defedare with certain instances because they simply don't agree with their viewpoint even if others may be interested in hear from other viewpoints, one instance may not want to update to the latest Lemmy version right away which means things might be slow or not work as well until they do update.
I'm sorry if you are looking for the actual specific difference between lemmy.world and lemm.ee, but ideally the administration of an instance should be transparent to you.
It's understandable to be confused. The easiest way to wrap your head around it is to think of it like the difference between Gmail and Hotmail, they both have the same purpose and do the same thing (showing you emails) but they are on different servers run by different people.
Lemmy.ml -- lemmy.world -- lemm.ee -- etc.
They are all servers that connect together. Some posts, pictures, and profiles are saved to one server, some are saved on another. All of that is accessible between all of them.
When I first joined, I never got a confirmation that my account had been accepted. After a few minutes, I just typed the username and password I used during registration and I was able to log in.
It's currently being worked on as a native function of Lemmy
https://github.com/LemmyNet/lemmy/pull/3480