They use the same protocol, but so far both of them have only implemented the server-to-server (federation) portion. Neither (to my knowledge) have implemented the client to server interactions.
Lemmy has its own API, which is completely separate from the ActivityPub spec. Kbin doesn’t have an API yet, but one is actively being developed.
I agree, standardization would be good.
It’s entirely up to the developers to collaborate and implement according to the spec though. ActivityPub wasn’t really designed with this use-case in mind, so the spec has limitations that warrant a specialized API, or extensions to the AP spec.
For example, the outbox is an OrderedCollection. This is how you would list posts in a magazine/community. However, there’s no way to sort by other metrics such as hot, top, or trending. Even Mastodon has its own REST API.