The OAuth2 JWT Profile introduces the possibility to use JWTs both as authorization grant and as client authentication.
The JWT client authentication feature is independent of a certain grant type, and can be used with any grant type, also the client credentials grant.
However, using the JWT grant type seems to do exactly the same as using the client credentials grant with JWT client authentication, except that the syntax is slightly different.
In both cases the client contacts the token endpoint to get an access token:
POST /token.oauth2 HTTP/1.1
Host: as.example.com
Content-Type: application/x-www-form-urlencoded
grant_type=urn%3Aietf%3Aparams%3Aoauth%3Agrant-type%3Ajwt-bearer&assertion=[JWT]
vs
POST /token.oauth2 HTTP/1.1
Host: as.example.com
Content-Type: application/x-www-form-urlencoded
grant_type=client_credentials&client_assertion_type=urn%3Aietf%3Aparams%3Aoauth%3Aclient-assertion-type%3Ajwt-bearer&client_assertion=[JWT]
A slightly different perspective on the great answer by Josh C: as it happens both the client authentication and the grant credentials can be expressed as JWTs but the semantics behind them are different.
It is about separation of concerns: clients authenticate with a credential that identifies them i.e. they are the so-called subject whereas they use grants that were issued to them i.e. they are the so-called audience. Or as RFC 7523 says:
The JWT MUST contain a "sub" (subject) claim identifying the principal that is the subject of the JWT. Two cases need to be differentiated:
A. For the authorization grant, the subject typically identifies an authorized accessor for which the access token is being requested (i.e., the resource owner or an authorized delegate), but in some cases, may be a pseudonymous identifier or other value denoting an anonymous user.
B. For client authentication, the subject MUST be the "client_id" of the OAuth client.