Usually what happens is your app, db, whatever will expose metrics (http request status, average response time, etc) in the Prometheus format which is then scraped by the Prometheus ingestor. The ingestor stores those metrics in a (short-term) datastore called TSDB. Prometheus also ships with a little web UI as well that can query those metrics in TSDB.
However Prometheus allows scraping from the ingestor (usually federation) or pushing into an external datastore that is usually more performant than TSDB.
So when people say "Prometheus", they usually are talking about the suite of tools however practically it's really just the format of the metrics data.