Bluesky doesn't have "instances", it has PDSes, Relays, and AppViews. People can run their own PDSes but PDSes are kind of invisible so you won't "see" them. You'll just see the whole Bluesky network as usual.
The bsky.app web app is a JavaScript app that runs in a browser. It talks to an AppView (API server) which talks to a Relay which talks to all PDS hosts on the network.