Not quite. An upvote on Lemmy is a favorite on mastodon. However, all posts on Lemmy look like they are a “boost” by the community when viewing from mastodon.

Good stuff! Thanks for all that you guys do for Lemmy and the open internet

That’s right. !Gaming@lemmy.ml is different from !Gaming@beehaw.org

Note that you can use your same account to subscribe to both of them, as one may be more active than the other. Feel free to pick one or both it doesn’t really matter. Different websites/servers have slightly different rules and different culture, so the posts and comments will be slightly different community to community.