With reference to the periodic table’s d-block, are the terms “transition metals” and “transition elements” interchangeable when describing these elements? Are there any situations where it would be incorrect to use one phrase instead of the other?
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").
In its preference for "transition elements" IUPAC may be bracing for a paradigm shift. Until now all d-block elements have had physical and chemical properties that qualify them as metals. But now, with the coming of the 6d block, we could see a transition element that is gaseous at ambient conditions and thus would not have the physical properties of metals unless condensed by cooling or pressure. We also see a mixing of late transition "metal" properties with noble gas properties here at what is normally a transition group (12), which to some extent is seen even for the 5d element mercury. The days of just transition "metals" are passing fast.