@ZipLine-- I'm not an expert on this topic but I don't think that stretch bandages are used for compression. Stretch bandages are usually thinner and apply little to no pressure whereas elastic bandages are thicker and made to apply pressure.
Like the article said, elastic bandages are mostly used for compression, to limit blood flow to the area. So it's used around or near a wound to reduce bleeding until the person can receive treatment at a hospital. I think elastic bandage could also be used in some types of sports injuries.
Stretch bandages on the other hand are used to keep dressing in place and clean. They are also flexible but have a looser weave to leave room for swelling. But they are not used to compress the area or reduce bleeding. Stretch bandages can be used on joints unlike elastic bandages.