A domestic short-haired cat is a cat of mixed ancestry thus not belonging to any particular recognised cat breed possessing a coat of short fur.
In British English, they are often referred to as moggies.
Domestic short-haired cats should not be confused with the British Shorthair, American Shorthair or other breeds with "Shorthair" names, which are breeds recognised by various registries.
Domestic short-haireds are the most popular cat in the United States.
Other generic terms include house cat and alley cat (the latter may be used more specifically to refer to feral specimens).
The term tabby cat technically refers to a coat pattern,
but is also often used as a general terms for cats of this sort.