We have a cow that just had twin calves, born seven days apart. The mother rejected the second calf. Would this kind of birth be called twins?
The classical definition of twins would require the calves to be born during the same parturition or birthing, so these calves do not fit that definition of twins. Certainly, the calves are not identical twins, as identical twins result from a cleavage of a fertilized ovum (egg) at an early cell division stage and are then carried in the same placental membrane and by necessity would have to be born at the same calving in order to survive.
These calves likely resulted from two distinct ova produced by the dam and fertilized at two different mating times. If the cow was only with one bull, then the calves are certainly full-sibs and could be considered as fraternal twins as they were carried in the same uterus of the cow.
This situation is not unique. Others have reported cows giving birth to two calves within a week, but it is rare. The calves could be sired by two different bulls; such calves are half-sibs but could not be considered as twins. It is likely that this cow ovulated and was in estrus (heat) at separate times, was serviced twice, conceived to each service, carried the two fetuses in separate placental membranes, and gave birth to the first calf without doing damage to the second calf's placental membrane, likely because one calf was carried in one horn (side) of the uterus, and the second calf was carried in the other horn of the uterus.