The easiest way to identify a twill weave is if the fabric appears to have a diagonal "texture"- this is caused by the offset of weft and warp threads when the fabric is woven (for example, over once, under twice. As opposed to over once, under once as a normal weave). The grain of the fabric is not actually diagonal, but the twill weave gives it that appearance.
A twill jersey is a type of sports uniform that is made of twill. Twill is a woven fabric with a ribbed pattern that is diagonal and parallel.
Cotton
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%.
A ribbed fabric is a fabric with intervening raised lines or ribs. Ribbed fabrics may come in a variety of compositions including cotton, wool and silk.
According to Wikipedia: Linsey-woolsey is a ". . . coarse twill or plain-woven fabric woven with a linen warp and a woollen weft."
Denim is fabricated from cotton twill yarn.
Woven cotton is exactly as it sounds. It is cotton that is woven and as such, has a flat 'finish' to it. Twill is made in such away that there are ridges, similar to corduroy, only usually much smaller. Also, the ridges run diagonal to the selvage, instead of parallel as it is in corduroy. If you were to compare quilting weight cotton, which is woven, with a twill cotton suitable for apparel, the twill usually will seem a bit sturdier. When I make purses from cotton fabric, I use quilting weight for the majority of the bag, but twill for the handles and the bottom of the bag, because I feel it has better strength.
Twill is a weaving pattern.
twill
Woven but look it up on wiki. Denim is a diagonal twill weave.
Oxford cloth, Stripes, Checks/Plaids, Twill & Woven Fabric, Broadcloth, Cotton Percentage of Dress Shirts Fabrics, etc.
Gingham is a woven fabric. It is usually woven of white and another color thread.