@fBoyle-- Yes, compression bandages are mostly elastic bandages. But which type you should use depends on what you're using it for. If you're trying to compress an area after an injury to prevent bleeding or to help healing after a sprain, then a long stretch elastic bandage is the right choice. If you're trying to treat something like leg ulcers, then a short stretch compression bandage is best.
Before using either though, you should check with your doctor first. If a compression bandage is used improperly or for too long, it can cause serious damage. It could cut off blood supply to limbs completely, eventually leading to necrosis or tissue death. If limbs, fingers or toes become cold or start looking purple, the bandage needs to be removed immediately.