Asian rhinoplasty versus Rhinoplasty, what's the difference?

The surgery and approach is the same. However, there are considerable differences in structural anatomy, soft tissue and skin characteristics of different ethnicities such as Asian, Middle Eastern, African American, Latino...Thus, some common maneuvers and techniques are often executed to achieve functional and aesthetica goals in cases of similar ethnicities versus others in very general terms but that doesn't undermine the individuality of each nose and surgeon's overall competence and experience in performing this complex surgery.

Asian rhinoplasty is an exceptionally challenging and demanding operation both technically and aesthetically. To achieve the best results in the safest, most predictable manner requires experience, technical excellence and artistry. 
There are a variety of techniques and philosophies when it comes to reshaping the nose during Asian rhinoplasty. One of the most important technical differences between surgeons is the use of artificial implants versus using your own tissue. I feel very strongly that the best way to achieve safe, permanent results is with tissue from your own body.Achieving the most attractive result will be possible by finding an experienced Asian rhinoplasty specialist who also shares your aesthetic goals. 

Your term "rhinoplasty" should probably be repackaged as a European rhinoplasty since rhinoplasties done by most American plastic surgeons are the direct descendants of the rhinoplasty invented in Berlin during the 1920's by Dr. Jacque Joseph.  His students immigrated to America and introduced these techniques which led to the beginning of the American/European rhinoplasty.  The American/European rhinoplasty was essentially a reduction rhinoplasty which currently has many excellent new iterations.  The Asian rhinoplasty is basically an augmentation rhinoplasty which, of course, also has exciting new iterations.  The Asian rhinoplasty is not a modified American/European rhinoplasty.  However, some of the basic techniques show a great deal of crossover.  In answer to your primary question (should I seek consultation from a plastic surgeon with expertise in the Asian rhinoplasty?), the answer is, of course, YES.  In America, because we are a melting pot, the signs of beauty tend to be a hodgepodge of multiple cultures.  We have taken the European rhinoplasty and added an American spin.  We also have taken the Asian rhinoplasty and modified it to fit our American perception of an aesthetic nose.  In my experience in Hawaii, Asian Americans tend to want more bridge, a narrowed nostril sill, augmentation of a retrusive maxilla, and addition of some sharp angles to the standard, soft round Asian tip.  Obviously, you need to seek consultation with a Board Certified plastic surgeon experienced in the Asian rhinoplasty.  Probably three consultations would be sufficient.  Evaluate these surgeons based on their before and after photos, reviews found on RealSelf, and your gut impression as to whether a particular surgeon and you can work together well to accomplish the nasal transformation you are seeking.