In general, even on humans it relates to the exterior mammary glands starting at the areola IIRC.
While general use may include the rest IIRC this was the reason why pasties could get around some decency laws. But as humans are one of the few mammals that have prominent protrusions absent actual milk production it is a bit hard to compare. Engorged breasts and outurned lips are the human equivalent of a peacock’s tail.
Tit derives from teat. At some point some men started shouting “show us your teats” at women, and their urban friends had no idea the word originally meant just the nipple. Teats, as the word for … teats, has been in use from the 12th century, according to m-w.com. Plenty of time for spelling and meaning to diverge and evolve.
It’s fairly common for people to use treatments intended for animals on themselves. For example I recall reading some years ago how an application meant to toughen up horse hooves was popular with women who wear long nails. Nails and hooves are made of the same material after all, and making long nails stronger reduces breakage.