Railway vs Supabase looks like a hosting decision but is really an architecture question. Railway is a deployment platform: give it any app — a Next.js server, a Python worker, a Go API, a cron job, a Postgres instance — and it runs the containers and wires them together. Supabase is a backend-as-a-service built around managed Postgres: the database plus auth, storage, realtime subscriptions, and auto-generated APIs, ready before you've written a server.
The overlap is narrower than it looks: both will host you a Postgres database, and that's roughly where it ends. Full disclosure, which is also a recommendation: Tiny Startups itself runs on both — the Next.js app deploys on Railway, and Supabase handles Postgres and file storage.