In iTunes on my Mac I have a “Drums” playlist which contains 16 songs. When I look at that playlist in Anytune Pro (on my iPad) I only see 10 songs. I have another general playlist in iTunes which contains over 500 songs. In Anytune Pro that playlist only contains 67 songs.
What most likely has happened is that those songs have not been downloaded to your iPad.
Try the following:
Open the Anytune settings, scroll to near the bottom and toggle ‘Show All Music’ to ON.
Most likely your tracks will show up now, but be greyed out.
Go into the Music app on your iPad. Open the Drums playlist. Take a look at the songs that are missing in Anytune. They probably have a download button on them (looks like a cloud with an arrow coming out of it). Tap to download the track. Now when you go back into Anytune it should be able to play them back.