Yes, crabapple is a species of apple. All eatable apples drives from crabapple several decades ago. Eatable apples has come to be called malus domestica, but that is not correct in a strictly biological meaning. If you seed sow seeds from eatable apples most of them will turn out to be crabapples.
Crabapples and eatable apples cross breed easily and are not possible to separate into two different species in a biological meaning. There are no pure species really, therefore it is most correct to call them Malus SP all off them.
In my realtives apple plantation they graft the eatable trees on the self sown crabapple trees. Quite an old method and not the most effecient. But really the only way given the soil conditions. Planting trees would just be too hard work in the rocky soil.
With eatable I mean tasty direct from the tree. All apples are non poisonous and can be eaten. Most crabapples makes good jam or cider.