As animuson mentioned, merges and synonyms are different.
Take a look at the tag synonym list.
Take a tag synonym that wasn't approved by a moderator, such as:
css -> max-width
This is a tag synonym. If you try to ask a question with the max-width tag, you will get the following tag suggestion:
You can still label max-width, but it recommends css and shows that the latter is a synonym of the former.
My understanding (and this could be wrong, I don't want to muddy SO with a test post), is that if you select max-width, after posting the question that tag will automatically be changed to css because that is the parent tag.
If you take a question tagged with one of the old tags, like this question tagged with timestamps (now a synonym of timestamp) and just edit it, the timestamps will be automatically converted to timestamp.
(I just did it for this post, please see the revision history).
In the synonyms list, you will see a column called "renames", this shows the number of times that the tag has been renamed to the one it is a synonym of (it was 3 for timestamp -> timestamps, now it's 4).
There are still 96 questions with timestamps, which will stay like that until someone edits them.
Take a look at the tag synonym list again.
Take a tag synonym that was approved by a moderator, such as:
accessibility -> a11y
You will notice that there are no longer any questions tagged a11y anymore, as they have all been merged in to accessibility. Furthermore, if I try to ask a question with the merged a11y I get the following tag suggestions:
This time I don't even have the option to pick the tag I typed it, it just automatically brings up the default one. (This could be because there are no questions left with the old tag in the system so it doesn't pop up)
Only mods can do merges. However, not all moderator-performed synonyms are also merges (although they often are).
Also, this is all non-official, but based on my understanding of the system.
This feature-request may also be helpful: Improving Tag Synonyms