The Fediverse is the loose network of servers that exchange data with the ActivityPub protocol. Mastodon is a server that implements a chunk of AP. Mastodon also specifies a client API that is not AP, but is fairly often implemented by other packages because it's convenient.
AP is not entirely Twitter-style microblogging. It can be used to exchange (data or links) photos, video, audio, documents, invitations and meeting appointments. The default privacy assumption for all AP content is that it is basically public.
Matrix is not built on AP. Matrix is a real-time communications protocol suitable for private messages and public chats. Its mission appears to be to bridge every other protocol, so there's at least one Matrix-ActivityPub bridge module, MXToot.
OpenID is not part of these. Some Matrix servers can use OpenID for authentication. As far as I know, no ActivityPub servers currently use OpenID.
AP is not entirely Twitter-style microblogging. It can be used to exchange (data or links) photos, video, audio, documents, invitations and meeting appointments. The default privacy assumption for all AP content is that it is basically public.
Matrix is not built on AP. Matrix is a real-time communications protocol suitable for private messages and public chats. Its mission appears to be to bridge every other protocol, so there's at least one Matrix-ActivityPub bridge module, MXToot.
OpenID is not part of these. Some Matrix servers can use OpenID for authentication. As far as I know, no ActivityPub servers currently use OpenID.