I read your question with interest. It does have philosophical dimensions, which I've tried to show below. I'm not sure how much we gain when we conceptualise hyocrisy (and the 'hypocrat') and demagoguery since they seem independent of each other. But you've made a start and I look forward to further contributions.
What is it to be a hypocrite? Gilbert Ryle's answer is the by now
commonly held one: to be hypocritical is to "try to appear activated
by a motive other than one's real motive"; again, it is "deliberately to
refrain from saying what comes to one's lips, while pretending to say
frankly things one does not mean." Can this be the right answer? My
aim is to show that it cannot. In doing this I hope to gesture towards a
richer understanding of our notion of hypocrisy.
Ryle's model for understanding 'hypocrisy' is that of the
self-conscious deception of others. The hypocrite uses "tricks" and
"talks in manners calculated to give false impressions" in order to
deceive others. While the charlatan pretends to skills he does not
have, the hypocrite "pretends to motives and moods" he does not
really have. (Béla Szabados, 'Hypocrisy', Canadian Journal of Philosophy, Vol. 9, No. 2 (Jun., 1979), pp. 195-210: 195.)
In ancient Greece, a demagogue was, literally, a "leader of the people." The
meaning of the term has changed considerably since then, however, and a
demagogue today is regarded as someone who "appeals to greed, fear, and hatred"
(Safire 163), a politician who achieves or holds power "by stirring up the feelings of
his audience and leading them [sic] to action despite the considerations which weigh
against it" (Scruton 115). (J. Justin Gustainis, 'Demagoguery and Political Rhetoric: A Review of the Literature', Rhetoric Society Quarterly, Vol. 20, No. 2 (Spring, 1990), pp. 155-161; W. Safire, Safire's Political Dictionary. New York: Random House, 1978: 163; R. Scruton, A Dictionary of Political Thought. New York: Hill and Wang, 1982: 115).
Lexical and conceptual analysis
The comment can readily be expected that the above is just dictionary work. So it would be if we were to say no more. But three conceptual points can be drawn out:
1.Hypocrisy does not imply demagoguery. The hypocrite may deceive others in a private context. Hypocrisy has conceptually no intrinsic political dimension.
2.Demagoguery in contrast does have an intrinsic political dimension. Both word and concept are inherently political. One cannot practise demagoguery in a private context.
3.Any use the demagogue makes of hypocrisy is purely contingent. The demagogue, who stirs up greed, fear, and hatred, may believe every word he or she says. There need be no concealment of real motive or any other resort to deception.
While I think that the question does invite conceptual analysis, as I've tried to show, I don't think conceptual analysis here throws much light. The two concepts are really independent and fairly obviously so on reflection.
If 'hypocrat' has a specific role in American political discourse - see J D's answer - its implication is, I take it, that Democrats (all or some) are hypocrites. In which case, they are (taken to be) a sub-set of hypocrites and to this extent, by implication, they fit the analysis of - fulfil the conditions for - hypocrisy that I offered at the start. I wouldn't make an en bloc moral characterisation of either of the American political parties but this takes us outside philosophy, a valid excuse for saying no more.