I am not sure that I know of any Ethernet (IEEE 802.3) standard cabling which uses solid-core wires rather than twisted-pair stranded wires. I can understand and see that many people consider "structured cabling" to consist of the former, but this article does not seem to mandate that construction, and indeed includes many types of twisted-pair and "patch" cables in the list of acceptable "structured cabling solutions."

https://en.wikipedia.org/wiki/Structured_cabling

So I believe that, in the realm of Ethernet in particular, "patch" vs. "structured" is not a useful distinction.

Yeah, it's not patch vs structured. Patch cables are part of structured cabling. But you won't generally find solid core wires outside of structured cabling, because they are inflexible, unwieldly and in many cases can't even be terminated with RJ45 plugs anyway (they are often too thick).

To regular people it's probably enough just to say Ethernet cable. Outside of structured cabling you don't really need to care and probably don't have a choice anyway. If someone says patch cable they probably know a bit about structured cabling and couldn't help themselves.

Within structured cabling the rabbit hole is quite deep. Even within a single standard like Cat6 there are many possible cable constructions with different types of shielding and wire gauge etc. It becomes important when you need the network to certify as Cat6 and support PoE in a high noise industrial environment, for example. And, of course, Ethernet can run over other cable types anyway, like fibre.