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If there's the same conversation shown on different kinds of Fediverse server, each server type will display it in its own format.
For example:
In the attached images, you can see a conversation thread in the replies to a PeerTube video post. On Mastodon it will look like a Masto thread, but on PeerTube it will look like comments below the video.
They are both the same thread! It's just displayed differently depending on which kind of server you're looking at it from.
@feditips now if only my mastodon account could double as a peertube account (for posting)
You can only use your account on the server where you registered, because each server is independent.