This terminology is tricky, and the fact that toast0 incorrectly thinks that this is a "stub resolver" is indicative of how people get this stuff wildly wrong. A "stub resolver" is in fact the client that makes requests of the server that you are asking about.
I use terminology borrowed from HTTP when explaining this to people. A DNS server that listens on a local IP address and makes back-end queries to another DNS server is a proxy DNS server, and the fact that it hands off all of the grunt work (of stitching together the back-end partial answers to make the front-end complete answers) to another proxy DNS server makes it a forwarding proxy DNS server. If it didn't hand off the grunt work and did all of the query resolution itself, talking directly to content DNS servers, it would be a resolving proxy DNS server.
And the software that is in applications, that formulates requests and sends them over to a proxy DNS server, is a DNS client library.
Stub resolver: A resolver that cannot perform all resolution itself.
Stub resolvers generally depend on a recursive resolver to
undertake the actual resolution function. Stub resolvers are
discussed but never fully defined in Section 5.3.1 of [RFC1034].
They are fully defined in Section 6.1.3.1 of [RFC1123].