By "heterogenous concept" I mean one that turns out, under analysis, to refer to multiple, distinguishable things. All I mean by "analysis," that I am not using in any sort of technical manner, is thinking about the meaning of the term (semantics and metaphysics often come to the same thing). Examples of heterogenous concepts from outside of philosophy of mind are value terms like "ethics" or "beauty," or for that matter very many abstract nouns such as (opening the dictionary randomly) "resemblance" or "reservoir." Heterogenous concepts are common (I'm not sure I even like the word "concepts." To me it feels like I'm just thinking about words). We can understand the continuity of meaning between "That man's reservoir of good will" and "The city's reservoir of water," but if we are thinking metaphysically (in the sense of our ontology) about reservoirs the two uses are different enough that (I would say) it makes most sense to say "'Reservoir' is a heterogenous concept," meaning that it is a word that refers to multiple, distinguishable things.
Once we are alert to the possibility that one concept-word can turn out to refer to distinguishable things we can sometimes clear the smoke away a bit from philosophical arguments. For example ethical theorists (not the best ethical theorists, but quite a few ethical theorists) might see themselves as involved in some sort of partisan contest: are the rights theorists correct (or better or what have you), or are the consequentialists getting it right(er)? Or maybe virtue theory is preferable to both? But wait: people can be "ethical" at a civil, legal sort of level (respecting others' rights), and "ethical" at a phenomenal, qualitative sort of level (minimizing felt harm), and they can be "good" people in the sense of being an example of a well-realized person. And in fact real good people (that is, good people when they're not doing philosophy) use Kantian-style "golden rule" reasoning and Millian outcomes-based strategies and they make Aristotelean evaluations of themselves and others, all at the same time, because "ethics" turns out to be a heterogenous concept. The intentions of self-aware beings and the phenomenal experiences of conscious beings and the health or pathology of living beings are all different things, such that there turn out to be not so much differences of opinion among "ethical theorists" as there are changings of the subject.
"Mind" is a heterogenous concept. Specifically, when people use the word "mind" they are sometimes referring to (using these words in their philosophy of mind sense) the intentional (beliefs, desires, hopes, fears), which is about persons and sometimes to the phenomenal (pains, tastes, sensations, tingles), which is about bodies. Thus we can use the same strategy that I just used to try to sort out "ethical theory" to try to sort out "theory of mind." Operationalist theories (such as functionalism) are addressing the problem of intentionality while materialist theories are addressing the problem of phenomenology. And both approaches work in their respective applications. Thus we can cut the contemporary gordian knot of philosophy of mind. That's why I am calling this project The Mind/Body Problems, plural.
One more point, about why it has been so hard for so long for people to realize that "mind" presents us with (at least) two metaphysical problems, not one. (Gilbert Ryle got this point right.) That is because most cultures and thus most persons have deeply internalized the ontology of the soul: one body, one mind. The body indisputably is something, some one thing, a very fancy physical object. The grammar (as Wittgenstein would say) of the word "mind," suggesting as it does that it refers to some one, individuated thing, combined with the idea that the mind is something separate from the body, creates a strong intuition (a wrong one) that there is one metaphysical problem here. And that has led to a great deal of heat and not much light at all.