Short answer first: use Supabase if you want Postgres plus auth, realtime, storage, and a dashboard as one managed bundle. Self-host Postgres – or use a managed Postgres – if you mostly need a database and your app already handles its own auth and logic.
The choice is not really "Postgres vs Supabase". It's whether you need the extra layers Supabase puts on top of Postgres.
Supabase is not a database
Supabase runs on PostgreSQL, but it's a stack of services around it:
Postgres – the actual database
