Transaxillary: an incision made to the axilla (armpit), from which the dissection tunnels medially, to emplace the implants, either bluntly or with an endoscope (illuminated video microcamera), without producing visible scars on the breast proper; yet, it is likelier to produce inferior asymmetry of the implant-device position. Therefore, surgical revision of transaxillary emplaced breast implants usually requires either an IMF incision or a periareolar incision.
The woman wanting a lift is usually slightly different. She had breasts she was happy with before, she had loving kids who she may or may not have breastfed, exercised and had a good life. They come wanting to restore the youthful breast they once they had(or better), they hate that it is slightly more deflated than before and it's slightly more south then they'd like. The formal name of this operation is "Mastopexy" and that's why you hear terms like "Mastopexy augmentation" because often in order to restore the youthfulness of the breast you not only need to reposition the nipple/areolar complex "up" with a mastopexy, you also need to provide some additional volume with an implant, hence augmentation as well. The discussion with implant also is entirely different discussion all together, but this highlights the primary difference in the reduction and a lift.
The FDA has identified that breast implants may be associated with a rare form of cancer called anaplastic large-cell lymphoma, believed to be associated with chronic bacterial inflammation. Similar ALCL phenomena have been seen with other types of medical implants including vascular access ports, orthopedic hip implants, and jaw (TMJ) implants. As of February 1, 2017, the FDA has received a total of 359 medical device reports of breast-implant-associated ALCL (BIALCL), including 9 deaths. Most cases of breast implant-associated ALCL had implants in for many years prior to the condition, and are usually treated successfully by simple removal of the implant and the capsule surrounding the implant without the need for chemotherapy if no evidence of systemic disease exists. If women with implants present with delayed swelling or fluid collection, cytologic studies and test for a marker "CD30" are suggested. The American Society of Plastic Surgery (ASPS) states, "CD30 is the main diagnostic test that must be performed on the seroma fluid as routine pathology or H&E staining can frequently miss the diagnosis."  Diagnosis and treatment of breast implant associated ALCL now follows standardized guidelines established by the National Comprehensive Cancer Network.