Bookmark has a different connotation. Also, bookmarks, unlike Likes, aren't public.

You were essentially correct - the Favorite button in third party apps got rewired to the Like heart button. Favorites were previously only visible to yourself, the person whose tweet you favorite, or anyone who specifically went looking for your list of Favorite tweets.

(I think making Favorites/Likes act like retweets was a terrible idea - thankfully I never saw them in third-party apps, but it made the website a horrible experience when you see what the people you follow were liking.)