Thank you for your question. Medical terminology can be confusing and certainly isn't intuitive. These two terms essentially refer to the same thing and in this case can mostly be used interchangeably. Rhinoplasty is surgery to change the shape or function of the nose. Nose reduction surgery would be a form of rhinoplasty just as alar base reduction is a form of alarplasty.
These terms are very similar and often times used interchangeably. A base reduction involves narrowing the width of the base of the nose and moving the alar sides inward. This is often times done along with alar plasty to reduce the length of the alar rim to maintain good nasal proportion and prevent a flaired nostril appearance after narrowing. Also alar reduction to reduce the nostril size can be done without adjusting the width of the base. It all depends on each individual's anatomy and their desired aesthetic outcome that determines which adjustments are best.
