Lemmy is the software that runs on all the servers. Lemmy.world and Beehaw are separately running that software. You make accounts on either server (just like you can make a Gmail account, or a Hotmail account), and do all the things with either account on either server.
Well, you could, but Beehaw basically blocked Lemmy.world. But otherwise the metaphor holds true. If you make an account on some other instance, you can subscribe to communities on Beehaw, post on Beehaw, and reply to users on Beehaw posts. When doing so your username, instead of being e.g. "mahogany", changes to "mahagony@[LEMMYSERVER]". That's how you can tell who is a user of that particular server.
Well, you could, but Beehaw basically blocked Lemmy.world. But otherwise the metaphor holds true. If you make an account on some other instance, you can subscribe to communities on Beehaw, post on Beehaw, and reply to users on Beehaw posts. When doing so your username, instead of being e.g. "mahogany", changes to "mahagony@[LEMMYSERVER]". That's how you can tell who is a user of that particular server.