Tor: What is the difference between Tor and Tor Browser?

Short answer

Tor is the underlying network and software for routing traffic through relays. Tor Browser is a browser configured to use that network and to reduce tracking and fingerprinting. Opening Tor Browser does not automatically send traffic from your other apps through Tor. Use Tor Browser for web browsing rather than attaching an ordinary browser to a Tor proxy.

Sources

Tor Project: About Tor Browser, Tor Project: Managing identities.