What's the difference between JWTs and Bearer Token?

Short answer

JWTs are a convenient way to encode and verify claims.

A Bearer token is just string, potentially arbitrary, that is used for authorization.

Context (story time)

A few years ago, before the JWT revolution, a <token> was just a string with no intrinsic meaning, e.g. 2pWS6RQmdZpE0TQ93X. That token was then looked-up in a database, which held the claims for that token. The downside of this approach is that DB access (or a cache) is required everytime the token is used.

JWTs encode and verify (via signing) their own claims. This allows folks to issue short-lived JWTs that are stateless (read: self-contained, don't depend on anybody else). They do not need to hit the DB. This reduces DB load and simplifies application architecture because only the service that issues the JWTs needs to worry about hitting the DB/persistence layer (the refresh_token you've probably come across).

JWT is an encoding standard for tokens that contains a JSON data payload that can be signed and encrypted.

JWT can be used for many things, among those are bearer tokens, i.e. a piece of information that you can present to some service that by virtue of you having it (you being the "bearer") grants you access to something.

Bearer tokens can be included in an HTTP request in different ways, one of them (probably the preferred one) being the Authorization header. But you could also put it into a request parameter, a cookie or the request body. That is mostly between you and the server you are trying to access.