How are wild dogs related to domesticated dogs?

I can tell you for a fact that hyenas aren't dogs. They're more closely related to cats actually, but they're a separate animal family of their own. Wild dogs, if you mean the African wild dog, belong to the family canidae as do dogs and wolves, but they are a separate genus, Lycaon. Modern thinking classes domestic dogs and grey wolves as the same species, canis lupus. You will see some older sources distinguish them as canis domesticus and canis lupus, but genetic studies have shown this is not valid.