I'm referring not to a recursive nameserver, but to a caching one that simply forwards queries to an upstream resolver. Like the one in every consumer router. Usually that's dnsmasq, with this option:
-D, --domain-needed
Tells dnsmasq to never forward A or AAAA queries for plain names, without dots
or domain parts, to upstream nameservers. If the name is not known from
/etc/hosts or DHCP then a "not found" answer is returned.
And the words that you are looking for are "resolving" and "forwarding". A proxy DNS server either does query resolution itself or forwards to another proxy DNS server that does. Both sorts can cache, so whether something is a caching server is not the distinction. dnsmasq is choosing whether to forward the query or to do query resolution itself (using a local data source) according to the number of labels in the domain name. As I said, at this level the idea of domain name qualification does not apply.
You are also mis-using "resolver", incidentally. The actual meaning of "resolver" per RFC 1034 is not what people sometimes think it to be. Avoid using "resolver". The mis-use creates confusion.