Cock is short for Cockerelcockerel. When a Cockerelcockerel is parkpart of a group of hens (roost) to encourage egg laying, it's called a Roosterrooster. I'd say Roosterrooster is more common in American English and Cockerelcockerel (Cockcock) is British English.
Edit, here is: Here in Vietnam, Cocks makecocks are sometimes pets like dogs,. I see Vietnamese take their cockcocks to the park or the riverside. They may spar them, not full on on Cockcock fights (though this may be more common than seen) so they are really Cockscocks not roostersroosters, as they lack a roost.