Perhaps I can shed some light on this for you.
In every day talk to say heifer (meaning has never been bred or calved) and to say cow (has had at least one calf) is correct.
But when you are selling or buying you need to be a little more specific as to exactly what you are selling or buying to maximize profit or reduce your risk.
It goes like this:
1. un-bred heifer (open) (buyer will use his own bull for breeding and take all the risk.)
2. bred heifer (covered) (bred to sellers bull, but as yet has not given birth.)
3. 1St time heifer ( open or covered) (bred to seller's bull, and has given birth.) Sold as "first time heifer with calf at her side". This allows the buyer the maximum number of future cows and heifers to breed to his bull later on.
It also gives him a quick return on his investment from the bull/steers calves which he will sell at weaning, while at the same time proves the heifers will breed and have no problems giving birth, reducing his risk. And it also helps with adjusting his next breeding season as he can wean early or late as needed and still have an income that year.
4. Same goes for second time heifers. This is just a little added insurance that the heifer will breed back after calving and have no problem calving the second time.
2nd time heifers is mainly to check if she will breed back after giving birth and how long it takes and may be sold as both 2nd time heifer (covered, bred AKA 3 in 1, just like the oil.) or calf by her side (bred by sellers bull).
After that they are generally sold or bought as "cows", open, covered or calf by their side.
The exact breaking point between heifer and cow is always after the breed back or 2nd birth, as all stages of her reproductive cycle have been proven at those points.
SL