I see a lot of surfactants which seem to exist both with a lauryl and a cocoyl tail, e.g. Coco Glucoside and Lauryl Glucoside, Sodium Lauryl Sulfate and Sodium Coco Sulfate, Sodium Cocoyl Isethionate and Sodium Lauryl Isethionate, etc.
My understanding is that Lauryl is strictly a C12 carbon chain, whereas Cocoyl means that the tails are similar to the fatty acids found in coconut oil, though they do not necessarily need to be derived from coconut.
Are there any generalizable differences between the cocoyl and lauryl versions of the same surfactant, e.g. one is milder than the other, one generally foams better than the other, ...?