Generally media servers (blossom) and relays are separate, but there is no reason why these two services can't sit on the same VPS or server.
Running a personal relay gives a great insight into what a relay is and how it works.
I spun one up from relay.tools to give me:
https://nortis.nostr1.com/
But I've never got round to running my own private strfry relay yet.

GitHub
GitHub - hoytech/strfry: a nostr relay
a nostr relay. Contribute to hoytech/strfry development by creating an account on GitHub.
You've now hit the limit of my relay knowledge, so yes I would definitely recommend running your own and understanding them better, then perhaps you can come back and tell me more about them.
Especially this Web of Trust stuff that I don't fully understand 😂