As one of the first to present the experience with local anesthesia (tumescent injection) to plastic surgeons, I can say with extensive experience in liposuction under general anesthesia as well as liposuction under local anesthesia with or without IV sedation, that the important thing is to understand what anesthesia is and what sedation is as well as the experience of the surgeon performing the liposuction.
Originally liposuction required general anesthesia as there was no other option and it involved a lot of blood loss so performing the procedure in an operating facility with an operating team, anesthesiologist, and surgeon was required. This made it difficult for non-plastic surgeons to perform the procedure and like many procedures, the costs and side effects of general anesthesia were significant so a search was on for ways to perform the procedure under local anesthesia in an office setting whether the operator was a plastic surgeon or had hospital operating privileges or not.
Tumescent injection for local anesthesia was actually developed by a non-plastic surgeon and it solved two problems. General anesthesia wasn't necessary to carry it out and it could reduce the amount of blood loss with the suction to nearly zero. Further study and experience showed that the large volume of extremely dilute local anesthesia used for tumescent injection was partially suctioned back with the liposuction and the remaining amount of local anesthetic and epinephrine was absorbed slowly and safely.
If the operating surgeon is experienced and comfortable with tumescent local anesthesia, the procedure can be done in an office setting with minimal sedation such as some oral medication and the patient can get up and walk at the end of the procedure similar to a dental or LASIK procedure. If the patient doesn't want to be aware of the procedure as for something like a wisdom tooth extraction or a colonoscopy, then an appropriately trained surgeon and staff can do IV sedation which is not anesthesia but aids the patient in dealing with the local anesthetic administration and carrying out the procedure. This can also be done by a nurse anesthetist or anesthesiologist but isn't required. The two major national plastic surgical societies, ASPS and ASAPS, require their members to have accreditation to perform procedures with local anesthesia and IV sedation in the non-hospital or outpatient surgical setting, usually an office.
I feel the patient should choose whether they want their liposuction done with local anesthesia and oral sedation or IV sedation or under general anesthesia, but the plastic surgeon may not be able to offer all of these options depending on experience level, accreditation, and preference. Interestingly, today even if liposuction is done under general anesthesia, tumescent injection is still used to minimize blood loss and postoperative pain relief.
To summarize, anesthesia means to put to sleep and this can be just local (the area operated on), regional (as an epidural or spinal), or general. Sedation is not anesthesia and is to sedate the patient to varying degrees for a procedure. With today's local anesthetic techniques and the drugs available for IV sedation, many procedures can be done comfortably and safely for the patient without general anesthesia.