Although lacking knowledge of internals of the `SX` model I have the impression, that 

 - clicking on the **close** link (let us call it `direct close vote) below the post either initiates a close review process (that is, added to the review queue at all, if it is the first close vote for that post) or just increments the number of close votes. However, this direct close vote does not count for the review queue badge (it that is important) and at least I my case, a direct close vote never appeared in my review panel, which is quite common sense, otherwise this would mean, to vote for close a second time on the same post.
The direct close vote link starts the review process. 

 - Voting for close in the review process increases your review count (unless skipped), regardless whether being edited/left open or closed. 

The direct close has an advantage, while being active, that it is possible to revoke one's close vote due to various reasons

 - The vote was just an error, being to fast with the clicking finger on the mouse
 - The OP edited the post, made it clearer, that it is not a duplicate, not too broad etc.

You cannot however, revoke the vote once made in the review queue (`reopen` queue has its own counter, so does not literally `count` as a revoke)