If I pay for Apple Music do I get Apple TV?

No, if you pay for Apple Music subscription you will get Apple Music only, but if get any of the Apple one plans tou will get music, Apple tv+ , iCloud storage and more depending of what plan tou get

If you are a student of higher education (as validated through UNiDAYS or SheerID), then you may apply for an Apple Music Student subscription, which includes Apple TV+ at no extra cost (until further notice), for countries and regions where both are available.

Access Apple TV+ with your Apple Music student subscription

If you have an Apple Music student subscription, you get access to Apple TV+ at no extra cost. Just open the Apple TV app and start watching Apple Originals. You can't share this Apple TV+ access with Family Sharing.