Transition metal or transition element?
Properly speaking, a "metal" is any substance with certain specific properties; chiefly, that it presents the charge transport behaviour of an electrical conductor. Since these properties are phase-dependent, it'd be more accurate to talk about "metallic phases" rather than "metallic substances" - as a given substance can present both metallic and non-metallic phases (to cite a famous, even if still not completely settled, example, hydrogen is thought to present a metallic phases, but not all hydrogen phases are metallic).

There are other ways to conceptualise metallic properties (such as a focus on band structure, or in terms of bonding) but these are pretty much equivalent to the definition that focuses on electrical conductor behaviour, as these are the underlying mechanisms that explain electrical conductors.

In any case, is it correct to identify certain elements as "metals", beyond talking about a specific metallic phase?

The answer is that no, it's not formally correct (IUPAC Gold Book prefers the term "transition elements"), but it is a well-established term, so when we refer to "metals" there is usually little ambiguity. Note that the term metal is also used in accepted definitions that focus on the properties and not on the elements (such as "molecular metal").