"Is there such a thing as a coydog?"

However, they are MUCH less common than people think. More often than not, a coyote would rather eat a dog than mate with it!
Also, coyotes have a limited breeding season (January through March) while dogs are fertile year-round.

The coyote/dog cross is a true hybrid, unlike the wolf/dog cross. Wolves and dogs are the same species and their offspring show no drop in fertility. This may or may not be the case for coyotes.

Is there a difference between coyotes/coydogs and wolves/wolfdogs?

I can only speak from my own personal experience, and the experiences of most coyote & coydog owners I have spoken with. However, I find that when experienced as a companion animal, overall the coys seem to have more challenging temperaments than Canis lupus (the wolf and domestic dog).
I lived with two high % coydogs and a reported wolf/coy/dog mix, and have read what little was available about them. I also spoke with other coyote & coydog owners whenever I got the chance, because they fascinate me--as most predators do.

Coyotes do only two things that wolves & dogs don't do. They have a "gape" when they feel threatened (hold their mouth open, like THIS), and they can make a hissing noise like a cat.

Overall, coys seem to have more of a "punk" attitude than wolves.
They're not really a 'pack animal', so they don't have the elaborate & well-developed social system and are naturally less cooperative, communicative, and readable/predictable. They did not evolve as "team players".
They're reactive like wolves, but seem to recover from it much faster. It's easy to see how they have quickly learned to live right alongside humans, unlike their more fearful wolf cousins.
They're more hyper. (Makes sense--smaller "dog"!)
Their pee smells worse than wolves or dogs...almost as nasty as foxes. Mine peed on EVERYTHING, constantly. This included toys & treats I gave them, in their water buckets when I filled them...and then they'd eat whatever they just peed all over.
They're also very territorial. My guys paced the borders of their enclosure relentlessly. I've heard from others who claimed to have coydogs that they can be very weird with strangers who visit the homeó-if they're not skittish, they can be outright aggressive about "intruders".

Coyotes are extremely opportunistic animals, and not as family-oriented as the wolves.
My younger coy cross switched alliances very quickly. He tried to take out his companion when he became old and weak, and later had to be penned alone because he had gone after multiple other animals--that he had always seemed to get along GREAT with--in their moment of weakness. He also developed aggression towards my roommate, once he realised that she was afraid of him.
On the plus side, my younger guy was *exceptionally* friendly, LOVED attention, respected confident humans, loved to play, and was a real character and a clown. He taught a lot of people that coyotes (often viewed as vermin) do have their good side and deserve a place in our world.

These observations are not set in stone, of course! Some folks have had fantastic experiences with both coydogs and full coyotes...and of course the lower the percentage and the further out from the last pure ancestor, the more doglike (and more laid back and "watered down") they will usually be. There's a lady on the west coast who breeds mid and low content coydogs, and hers are great--she takes them out as ambassadors. :) They have enough coy to be clever and personable and fun...but are not as intense as the full coys.

My notes are simply to relay what seems to often be the case for coyote-acting animals--your "starting point" with them, so to speak, and the things you may need to be prepared to work with.
The book "Shasta and Rogue", a true story about the lives of two full-blooded pet coyotes, may be of interest as well.

Coyotes and coydogs, like wolves and wolfdogs, are usually misrepresented. The vast majority of reported or claimed "coydogs" are not coyote crosses at all, but simply husky or German shepherd crosses that look vaguely coyote-ish to the untrained eye.

Here are some actual coyote x dog crosses:

(This last one was crossed to a beagle!)

Here are two links showing intentionally bred coydog lines:

Sundance Ranch
Alune's beautiful coydogs (historical info only)

Coyotes can also interbreed with wolves. There are two separate animals that most likely resulted from this: the Eastern coyote

and the Red Wolf.

For comparison, here are some pictures of full blooded coyotes.

coyote photos

more coyote photos

These, in contrast, are NOT coydogs--at least not of any significant coyote content. They are simply mixed-breed dogs represented as or "guessed to be" coyotes or coydogs...by rescues, veterinarians, or pet owners who felt they had a "coyote look" to them.

It should be fairly clear when compared to the actual coyotes and coydogs above, that these softer-looking and less primitive canines do not have recent wild heritage.