The Debian tor service you refer to is actually just a tor service file which is owned by the debian user. The service file is part of systemd and allows you to start and stop tor as well as get its status as you’ve done with ‘sudo service tor status’ You can get the same output with systemctl status tor.
The service file allows you to launch tor efficiently at boot time, or for tor to be launched by other services. You can also disable tor from running with systemctl if you so wish. More information on that is in the systemctl man page; man systemctl look for ‘disable’.
Tor itself, the process that tor.service launches, is described this way -
Basically, Tor provides a distributed network of servers or relays (“onion routers”). Users bounce their TCP streams — web traffic, ftp, ssh, etc. — around the network, and recipients, observers, and even the relays themselves have difficulty tracking the source of the stream.
There’s more information on Tor’s web site. Hope this helps.