In the Context of OpenID Connect, when someone says send me the JWT, it is not clear whether to send the access token, the id token, or some other payload. It would be more clear to say send the access token or send the id token or even please send the access token, which happens to be encoded as a JWT.

Access Tokens may be JWTs.

Access tokens can have different formats, structures, and methods of utilization (e.g., cryptographic properties) based on the resource server security requirements.

ID Tokens must be JWTs.

The ID Token is represented as a JSON Web Token (JWT).

Bearer Tokens are Access Tokens

When sending the access token in the "Authorization" request header field defined by HTTP/1.1 [RFC2617], the client uses the "Bearer" authentication scheme to transmit the access token.

JWTs are a way of Encrypting/Signing JSON payloads

... enabling the claims to be digitally signed or integrity protected with a Message Authentication Code (MAC) and/or encrypted.