You and I are posting on the Fediverse right now (capital F). If I create two of my own personal Lemmy instances that only federate with each other, they’re not a part of the Fediverse. I’ve now created my own fediverse (lower-case F). The Fediverse is a fediverse, but not all fediverses are the Fediverse.

Same with internet and Internet. There is the main, collective Internet that we all know and use daily, but it’s one of many internets.