Is there any difference between restoring an app and installing an app on an Android device, or are both the same?
As David said, you can restore an unsupported app from a previous backup, or you can restore the data of that app ( e.g. saves in a game ). when you install an app from the play store, you are limited to what's available for your country (unless you're rooted then there some ways to go around it) and even if you install an app that you previously had, the data will not be restored.
google play store just backs up your apps names so when you restore through the play store, the data is not restored.
Well, one that comes to mind - if application is removed from market or is not listed as compatible for your device, restoring from Google account is one way of getting those applications. I did it with "FML official" and "Amazon" applications when they were not available on Nexus 7 2013 - "backed" them up on my Samsung S2 and "restored" on Nexus 7.
And, of course, for some applications settings are restored too.