Federation: your post on lemmy.world is downloaded by my instance, my reply is sent to yours.

Defederation: your instance (through its admins) decides to disconnect from mine, I can’t see or interact with your stuff unless I make an account in your instance.

Fediverse: all of the different platforms that support federation (often with ActivityPub, but there are other protocols). Lemmy, mastodon, Pixelfed, Bookwyrm, etc. See: https://joinfediverse.wiki/What_are_Fediverse_projects%3F

Cross-platform I would typically assume refers to different platforms being able to talk to each other using ActivityPub, like Lemmy and Mastodon can do. Features may work but with quirks because of the ways they implement protocol. How well one platform works with another is actually undefined unless work is made to make them compatible. An example is Lemmy and Kbin, originally their upvotes and downvotes used different features of the protocol and were not compatible.