Downloaded an app on itunes through computer, didnt download on ipod touch.

I bought an app on my computer through Itunes, and it completed the download, my ipod touch has the app, but not downloaded, I tried tapping it to restart the download, but it wont, does that make sense? i'm not very tech savvy, if anyone understands a little about what i'm saying maybe you could be quite useful, thanks! 😐