A more than likely scenario is that the two tunes you have versions of are actually the same tune, but whoever was in charge of getting the licenses for the release of the one of the records screwed up and credited the wrong version of "You're My Thrill". It's easy enough to do. When getting licenses for the seven cover tunes on the upcoming Root Doctor CD, I ran into about 10 different tunes called "Mississippi Blues". I used the information from a Rory Block CD to find the correct writer (thus realizing it's in the public domain), but if her CD is wrong, then I'm wrong as well. You can see how this perpetuates itself.
Licensing turns up interesting things. For instance, one of the cover tunes we do on the Root Doctor CD I thought was called "Love Bone" (originally done by Johnnie Taylor) and on most CDs that cover it, that is what it is called. But the real title of the song I found out is actually "Love Bones". Same thing for "Turning Point", originally done by Tyrone Davis. The real title is "The Turning Point", but even on his album it's called "Turning Point".