Is it not fair to say that this is the same thing? My impression was that in designing a compiler you're explicitly determining the rules for language, which is the same as designing the language itself? Or do you mean that technically the compiler, not the language, is JIT?

This is a new area for me so apologies if I'm just misunderstanding the mechanics here!

This is true in the same sense that "a JIT" should really be "a JIT compiler."

Used as "a JIT," the term is given new meaning (to refer to a compiler implicitly). And used as "JIT language," its giving the term a new meating (to refer to the fact that the language designed to be JITted).