Mastodon

If someone on server B were to boost that posts from server C, then yes they'd show up on server A as far as I know - but only if they're boosted. The federation aspect works a lot like Lemmy's, so while my instance my federates with lemmy.world (and vice versa), my instance doesn't know about the communities on LW unless someone on my instance subscribes to that community in particular (and vice-versa for a community on my instance not showing up on LW until someone over there subscribes). At least, that's how I understand it - to be honest I still don't have my head completely wrapped around Mastodon's federation aspect but since both Mastodon and Lemmy use ActivityPub I'd reckon that they're very similar.