There are still more layers of complifusion over this.
Live animals are commonly known by gender-specific names, e.g. cow and bull; ewe and ram; mare and stallion. Served on the plate, there don’t seem to be separate names for gender. “Beef” doesn’t tell us if said beef, in its former life, was cow, bull, or steer.
Furthermore, animals (and some foods, as discussed already) have separate names according to the age of the animal.
Look how many words we have for “horse”, just according to age and gender:
Foal, colt, filly, stallion, mare, gelding.
I am surprised that no one has mentioned lamb. Historically in England, sheep were grown for their wool, which (with derived products) accounted for some 75% of Tudor English exports. Mutton (mouton) was from a sheep that was too old to produce good wool (unless you were rich).
In modern times we almost never see mutton, it is always lamb. There seems to be a variety of definitions of ‘lamb’ but one I heard was a sheep in the year following its birth year, so up to twenty-odd months then.
It is pretty obvious that ‘lamb’ seems somehow more desirable than ‘mutton’ and I strongly suspect that is is butcher’s that have driven mutton off the shelf while still selling the same meat that would once have been called mutton.
A lamb, strictly speaking, is under 12 months old, and does not yet have its permanent teeth. The meat of this animal is sold as “lamb”.
A hogget is over twelve months old, but still hasn’t reached a particular stage of dental development - I forget the details; it has something to do with the number and of permanent teeth. A hogget will be under 24 months. This animal is sold at market as hogget, but its meat is sold as lamb.
Anything older than a hogget is a sheep or, rarely, a mutton, and the meat is sold as mutton (except in the US, I think, where it’s sold as lamb).
In written English, I’ve rarely seen “beeves” in the mouth of an American (a cowboy, for that matter), but “veals” only in the mouth of Viz character “Student Grant”, and the whole point was that Grant was woefully ignorant about the animals whose rights he was demonstrating for.