how to know my MacPro 5.1 (mid2010) is a server?

The models sold as Server just had a very-slightly upgraded hardware configuration, which you could easily have upgraded to (or beyond) if that was the hardware setup you wanted. They are NOT magical special Hardware.

MacOS Server is a separate software Applications, and it requires a substantial investment of time and energy to get it running properly. If you are not deliberately running "Server.app" your Mac is an ordinary Mac, not a Server.