Labiaplasty, to us, is more of an aesthetic type procedure where you're trying to make the area look better. Vaginoplasties imply more serious procedures where you're trying to tighten the vaginal orifice and do a lot more internal work. The labiaplasty is mostly external.
Labiaplasty or Vaginoplasty: Internal or External Repair
Dr. Curtis Wong explains the difference between an internal vaginoplasty and an external labiaplasty.