Twill is fabric that has a diagonal pattern. It is actually woven in such a way as to create diagonal “ribs” in the fabric itself (not just colored diagonal lines). Think of cordoroy – that is a fabric with a vertical (up and down) pattern woven into it. Twill is diagonal weaving. If a twill fabric has extra “give” so that it can expand (stretch), it is a stretch twill.
Stretch twill often refers to the fabric having a small percentage of lycra/spandex in it, usually 2-4%.