Regular edits are immediate, and you only get a notification about those after they changed your post.
You can only approve (or decline) suggested edits by users who do not yet have the required editing privilegesediting privileges to perform regular edits. These are placed in a queue for review by more experienced users, and only actually performed once approved.
So, yes, there is an approve button, but only when the editing user does not yet have at least 2000 reputation.