But in English we would say " we are celebrating ten years of"...marriage...or something
You're right to be confused though because no with English as their first language would say "we celebrate 10 years"
They're almost the same thing. The only difference is that sărbătorim comes from sărbătoare(holiday) and aniversăm comes from aniversare(anniversary).
In my opinion sărbătorim is more general while aniversăm refers to a repeatedly recurring date. So I would say noi sărbătorim Paștele (we celebrate Easter) but not noi aniversăm P.