They are both terms used to designate the female bovine. The generic term “cow” is considered more correct in the zootechnical field.
“Mucca” instead, probably derives from the affectionate German term "Mugg" or "Muggeli", which indicated the Swiss dairy cows, purchased at the livestock fair in Lugano and imported into Italy. Italian breeders kept this name to differentiate these cows, considered more valuable than the native ones.
Today the term “cow” is more used, as in common language “cow” has taken on a negative connotation.