lemmygrad.ml, lemmy.ml, etc. are instances of the Lemmy software run on different servers. The lemmygrad.ml instance has its set of communities (this is /c/communism, which you’ll see as /c/communism@lemmygrad.ml if you’re visiting through lemmy.ml), and the lemmy.ml instance has its set of communities (for example, /c/anarchism, which Lemmygrad users see as /c/anarchism@lemmy.ml). Since lemmygrad.ml and lemmy.ml are connected, users can post in the communities in either of the instances (unless they’re banned on one specific instance/community). There are many other instances, but these seem to be the two biggest ones, unless you include Hexbear (AFAICT, it uses a modified version of the Lemmy software, so it can’t connect to normal Lemmy instances yet).

I’m not sure about other clients (for Android, etc.), but the web interface used by lemmygrad.ml and lemmy.ml lets you view posts on your own instance only (“Local”), or on all connected instances (“All”).