Apple released iTunes 12.5.2 recently to fix a problem with play order and squash a bug related to lyrics and Beats 1 (see “iTunes 12.5.2,” 28 October 2016).
However, many people were surprised when the App Store app started offering iTunes 12.5.3 shortly after that, with exactly the same release notes. Checking iTunes > About iTunes revealed that its extended version was iTunes 220.127.116.11.
A day later, those who had installed 12.5.3 wondered if something had gone wrong when the App Store app prompted them to install iTunes 12.5.3 yet again, with those same release notes once more. That version identified itself internally as iTunes 18.104.22.168.
We have no idea how these three versions might differ, but it isn’t related to anything you’ve done — Apple bears full responsibility for the confusion.
If you installed iTunes 12.5.2, it’s almost certainly worth installing the latest version of 12.5.3, under the assumption that whatever the changes may have been, they were so small that it wasn’t even worth moving the version number to 12.5.4.