Yes, they're different things. However you need a place to live so unless you already own a paid off house, you can choose between paying a rent or paying a mortgage.
It's the bigger part of your "housing costs" in both cases.
Yeah I know. The point is the comparison is not really mortgage vs rent. From a purely financial perspective you're paying mortgage + owning costs + rent opportunity cost + liquidity risk.
If you can pay a mortgage most likely you can pay a rent, and it's going to be way cheaper if you factor everything in. And in both cases you can be evicted if you don't pay anyway.
It's the bigger part of your "housing costs" in both cases.