There used to a slight difference in the sleeve surgery, but very little, they just started calling it vertical sleeve because it is a better visual tool for patients. The difference between the two is that there is only part of the stomach taken out with the sleeve surgery, leaving you with a 'vertical tube' in which food still travels. They don't mess with your switch, which is what is at the bottom of your stomach that holds and releases food from the stomach to the intestinal track. therefore, you still run the risk of overfilling your 'sleeve' and stretching it out, reducing or eliminating your ability to lose weight over time, hence the success rate of only 50% of patients over 5 or more years.
With bypass they do exactly that, they remove a large portion of your stomach, remove a section of your small intestines, taking the 20 feet and removing between 5-10 feet of it, then they 'bypass' your switch and reattach your small intestine to the 'pouch' they created right below your esophagus. Since you no longer have a functioning switch, food passes through you quickly, and you are also now in a constant 'malabsorption' state because you have less small intestines to absorb your food as it passes through, which makes taking your daily vitamins and minerals more important.
The duodenal switch procedure is completely different from both and is the most effective at weight loss, but also the most malabsorptive as well.
When doctors are determining which procedure to go forward with, it is primarily based on what they think you need for your personal medical needs. Most get the sleeve if they aren't suffering too many detrimental health problems and only have a somewhat mid amount of weight to lose. It is slow and steady weight loss. Bypass is more common when there are multiple medical reasons for the weight loss, such as diabetes, GERD, heartburn, acid reflux, high blood pressure, etc. as it can reverse those symptoms on top of weight loss. It is also more effective at keeping the weight off at a 75% success rate, due to the fact that the switch is bypassed and the tool is more effective. It is used for patients needing to lose more than 150+ lbs. typically with some type of medical need as well. The weight loss is fast then stalls, then fast then stalls and can take more than a year to get to a goal weight. The DS surgery is for extreme weight loss, but only for patients who can follow a regime as the vitamins and calcium are needed or they end up in the hospital with the high malabsorption rate that is caused by that surgery. Typically patients needing to lose more than 300 lbs. have the DS done. It is usually fast weight loss for a steady 2 years with a high success rate at 85%. Of course, all WLS surgery is based on insurance and what they will and will not cover which is another hurdle WLS patients face as well. Unless you pay cash, you get what you get when it comes to relying on insurance. If your insurance can prove the medical necessity of the procedure, it will cover it.