The wolf (including the dingo and domestic dog), coyote, and jackal, all have 78 chromosomes arranged in 39 pairs. This allows them to hybridise freely (barring size or behavioural constraints) and produce fertile offspring.
The domestic dog (Canis lupus familiaris) is a domesticated form of the Grey Wolf (Canis lupus lupus), and therefore belongs to the same species as other wolves such as the Dingo (Canis lupus dingo). Therefore crosses between these sub-species are unremarkable, and not a hybridization in the same sense as an interbreeding between different species of Canidae.
There is no genetic difference between a male coyote/female dog breeding and a male dog/female coyote breeding, but two separate terms have been invented, coydog and dogote, for unknown reasons. A major difference between the two is logically the birthplace of the offspring: a female coyote would give birth in the wild and a female dog, unless feral itself, would give birth domestically.