Midline is when they lie the cat on their back & cut them down their abdomen/tummy. Flank is when they lie them on their side & cut in on their side.

Vets should be able to draw blood by wetting the fur instead of shaving. I didn't know any of this & my vet did a midline & minimal shaving for her spay (none on her legs). She had an operation a month ago & this time the vet took blood from two places & shaved nearly all her underside & it is really struggling to grow back! Though she is a semi-long hair & a mature one at that.