First of all, it has one big difference: What types of communities you see when you browse the "Local" communities (on most apps or web UIs it's gonna be a setting at the top). "Local" shows you threads posted in communities that are on your instance; "All" shows you the whole network, similar to /r/all on reddit; and "Subscribed" shows you only the communities you're interested in, similar to the main page on reddit. It makes sense to switch this setting to All for the time being, and to see what's going on everywhere else and which communities develop; to Local when you get confused, e.g. with lots of posts in languages you don't speak or lots of duplicate posts; and to Subscribed once things have settled down and once you have found your communities that you're interested in (and other stuff that you're not interested in becomes more and more on the All feed).

There's some eceptions when the "linked instances" structure does make a difference:

during heavy development (like in the early stages right now), federation might break here and there (for example right now between some servers using on older version of the Lemmy backend and those that already updated). also, there's probably gonna be multiple similar communities on various instances (nearly every instance has a "main" community and a "Lemmy discussion/reddit bashing" community). this will all settle down with time, federation in general will be more stable, and "main" communities will develop, with smaller alternative ones spread around that can take over if the main one is taken offline.
when instances decide to "defederate" from each other. this is a conscious decision by the admins (standard setting is to share everything with everybody else, but specific instances can be added to a blocklist). this means their content doesn't show up on your instance, and users from those instances can't interact with one another anymore. this happens at the moment with lots of NSFW instances and the more tame ones, but once moderation tools are improved, it will settle as well.

Quick tips: Don't be too stressed about "missing" content on other instances, right now it's still early days and a bit chaotic. And do consider making multiple accounts on other instances, and checking out what's different. the apps that are being developed right now make switching between multiple accounts easy, and one day will hopefully bring bookmarks and comments across multiple accounts together as well. Shop around for different instances and apps and see what's out there,, read people's recommendations, try and find instance and community lists. And in general, don't see your current account as the only way you'll interact with the Lemmy network (just as alt accounts were a thing on Reddit), and don't expect the network to serve you everything on a golden platter, you'll have to do some hunting around for the cool things, a bit like in the internet days before Web 2.0 happened – but that's half the fun!