I have to disagree with you about Cthulhu monsters being very similar to the Horrors (or demons being similar). Cthulhu monsters, in general, do not care about the fate of humanity. This is stated (or implied) several times throughout Lovecraft's works. Yet they always seem to hang around to torment humans, or be the object of worship for a cult, or whatever. They have what I call "active disinterest" in humanity, to the point of one walking up to your door to borrow a cup of sugar, but without all that bothering to knock and ask you for it. It's really perplexing, even if the stories themselves are interesting and well written.
The concept for Cthulhu mythos creatures is actually quite simple and direct: they are several stages of development (mystic/psychic, one would assume) above humanity. They are, to us, what we are to, say, cockroaches; amoeba or paramecium might be even better. They don't particularly care or need to care about (or even notice) our existence. We would not think about accidentally stepping on a one-celled organism, breaking into its house, or just living in the same place as it; we would not even be aware that they have a society, much less what some fragment happens to be doing (e.g. worshipping us) while we're going about our daily business. And with Cthulhu-mythos beings, the impact of the power of their psyches, even from the 'least' of them, causes enormous amounts of stress and can lead to psychotic breaks and other forms of insanity. It isn't a matter of intent, it's a matter of power levels. So yes, I would agree with you that Cthulhu monsters are not quite similar to Horrors; the Horrors, of all types and levels (right up to the Great Hunter himself) would themselves be several levels below those of the Cthulhu 'group', just due to their attachment to humanity. I'll agree that paralleling Cthulhuae (??) with Horrors may be a sub-ideal comparison.
Demons want to torment humanity because they are evil. Period. That's it for motivation, they don't get any deeper than that. Demons will eat someone's legs because, oh ho that's really viscious and nasty and EEEeeevilll!! I can't write anymore about them because they don't have anything else there. They are really a very dull antagonist.
Err, well, no. That's emo goth 'bad person' wannabes.
Demons -- if we're presuming these are those angels who rebelled in Heaven and chose to Fall instead of humbling themselves and accepting YHVH's forgiveness -- desire to torment, mislead, and cause the downfall of humanity because of a
philosophical disagreement. Depending on the starting point, either Mankind either needs to be saved in its entirety (and the demons so torment us in order to prove a point against the whole 'each must make choices throughout life') or else Mankind does not deserve to receive such love and attention from YHVH (and the demons so torment us in order to display why they are unworthy of that attention. It isn't hunger; it's politics. A demon wants people first and foremost to Make Bad Choices, i.e. to sin, and will use any and all methods of persuasion -- conversation, debate, enticement, seduction, blackmail, threats, violence, torture, &c. -- to push their victim into committing sins. They are defined as evil by humanity and the Heavenly Host (who have written the history books); they themselves do not define themselves as being evil, except in the most whinging sorts of writing.
Comparing demons with Horrors is, again, sub-ideal; it'd be like comparing a person with a dog. The person is shooting the rabbits because they're eating his crops (the philosophical reason), and the fact that he
can eat them is a secondary benefit; the dog attacks them purely because he's hungry.
Horrors, OTOH, are much better villians and antagonists. They have a reason for coming to the Earthly plane, one that is easily understandable, even if their methods are not: Food. Perhaps it's harder for predators there to get sustenance without great risk, and so "our" world looks like a garden ripe with fruit to them. It may be a simple motivation, but it is one that makes far more sense than Cthulhu mythos ("We don't care about you, FEAR ME!!") or a demonic invasion ("RARR!! ME EVIL!!").
Speaking of evil, the Horrors are undoubtably evil, but not because they are Evil (twirl that mustache!), but because they perform evil actions. This is a crucial difference, and one that makes them a better foil. A monster that is evil because it is what it is (demons) is not nearly as interesting to read about, or fight against. Since they do have a clear motivation for their actions, they can be bargained with (not recommended), or someone can use that motivation against them. A clever hero can use their wits to thwart them, and not because a Horror is dim (often they are not) but because their motivation is something that can be understood and used.
IMO, Horrors are a far more interesting and useful antagonist than any mere Cthulhu creature or demon.
And I accept your opinion. In mine, Cthulhuites (?? -- what IS the right term for the entire lot of 'em?) are interesting the way natural disasters are interesting, as an examination of humanity by how they react to an extreme situation. Horrors are interesting because despite their sentience, they are still motivated by that one thing, hunger; all they do is derived from the desire to satisfy that one need, in all its myriad forms. As you say, they can be fought against, thwarted, redirected, tricked, etc. -- but in essence and my opinion, fighting against even the most powerful Horror is to battle a near-sentient creature with a singular aim.
Demons, again in
my opinion, are the hardest and worst of the lot -- because they are out to cause you to corrupt yourself. They don't need you to beat yourself up over it the way Horrors do (because that anguish is the Horror's bread-and-butter); they just want you to do it, because in so doing you are proving their point, that you don't deserve either a) free will, or b) redemption. Or c), both. They are the hardest to fight, because you aren't fighting them, you are fighting
yourself.
So no, demons and Cthulhu beings do not quite parallel Horrors; in both cases, the Horrors are lesser than those they are being compared to, In a generalized form, however, all three can be considered 'wholly alien' to the human condition; beings from 'elsewhere', with powers far beyond what man has, and who torment/torture humanity for reasons of their own (or simply as a side effect of going about their own business). This is the point that James indicates, not the nitty-gritty of how and why.