Below are some pics of the the two surgeries.
In the DS, the pyloric vale remains in its normal position at the exit of the stomach, and still keeps on doing its job, just like it does pre-op. In the RNY, the pylorus is bypassed---it remains a part of the remnant stomach, and does nothing.
In the RNY, the pylorus is replaced by the stoma, a man-made, always-open hole. Normal stomach functions cease---the pouch does NOTHING but store food for a while. Over time, the stoma can stretch, and when that happens, no more restriction. ANd so far, no one's found a really good way of repairing a stretched stoma.
Even when functioning properly, the stoma is the main reason for dumping syndrome---undigested food enters the small intestine in a place where, in normal anatomy, undigested food NEVER goes. In some people, with certain foods, this causes an unnatural insulin reaction that has nasty side effects.
The stoma is also largely responsibe for so-called 'late dumping', more properly known as reactive hypoglycemia. For some people, this never happens. FOr others, it's very mild, and/or easily controlled by diet. FOr others, it's more severe, and while controlled by diet, it requires a VERY strict eating schedule and very strict eating protocol. For some very few people, it's a completely life-altering event.
Loose stools. Well.
This is, for most people, totally diet-based. The more fat one eats, the looser one's stools tend to be, since about 80% of the fat a DSer eats goes down the toilet. How much fat is too much varies from person to person. Too little fat can cause constipation. I'd guess that about 98% of DSers find a happy medium and have comfortable bowel habits.
Loose stools can also be caused by bacterial overgrowth or other medical issues. Sometimes bacterial overgrowth can be cured by probiotics, but sometimes a round of antibiotics are required, followed by probiotics to restore the 'good' bacteria. The other medical issues are so rare and so diverse I'm not going to go into them here.
The most important thing you should know about the difference between the RNY and the DS is the long-term, maintained results. The DS has far better ones. (*grin*) Equally important to ME was that the post-op DS eating plan suited me far better.
Here's a pic of the RNY:

And here's a pic of the DS:
Well, here's a clearer one: