^Zyoptix is just a machine. Its one of the best out there, and with highly satisfactory reviews over the period of time. Zyoptix also have had a series of machines. The one I got done under was Zyoptix 100.
All machines use the same method of creating a corneal flap and reshaping the cornea with a cold excimer laser beam, i.e. LASIK - read up the name on google.They are only getting more and more precise and safer over the period of time.
Regular LASIK doesn't take into consideration the size of your pupil, it sculpts the area around it. Regular LASIK is suitable if your pupil doesn't dilate much during the night, otherwise problems of halos and glaring occurs.
Wavefront, aspheric and customized LASIK is for people who face higher dilation of the pupil during low light condition, and hence the machine programs the laser to sculpt a very specific area around the pupil. This is the way to go if you don't want to experience glaring and halos at night.
Tissue saving method is for people with low corneal thickness or with very high myopia i.e. greater than -10 diopters, since higher the diopter, the deeper the laser ablation occurs.
Since I had low myopia, I had very little corneal thickness loss ( and I already have a thicker than normal cornea). My pupils also do not dilate much in the night, so I didn't have to go for customized lasik.