I'm going down the same rabbit hole and have struggled trying to figure out the fediverse. The other comments on your post explain things well. From my experience, I had to research which instance was federated and populated with what fits my interests, then sign up for it. Jerboa doesn't do well with it's search function yet, and I almost exclusively use the app to browse (I did so with Sync for Reddit ((3rd party app)) too and never used the browser unless I was looking up specific questions), but I did find out that when using a web browser to login to my instance they have a community browser that lists every and all communities locally and federated where you just hit Subscribe to. Once I subscribed to everything that peaked my interests I went back to my app (Jerboa for Lemmy) and sorted by Subscribed and New (or hot). I now have an experience very similar to that of using Sync for Reddit.

To answer your questions about seeing the exact same communities (instead of a singular subreddit) to subscribe to, it's just because each community is hosted on separate instances. Some of those instances are federated with yours (ie lemmy.world) but for users who are signed up on that particular instance may not have the same federations your instance has so they created their own version of the community.

Another comment on this post explains it well using minecraft as an example. (Idk how to cross-post or @ another user yet)