Both are woven fabrics. 'Jacquard' is the name of the automated loom, capable of many vast and different designs not acheivable on an ordinary hand or dobby loom. Damask fabric (not a loom, more a type of design) has one warp and one weft only. Jacquard fabrics can have up to two warps and anywhere from 1 - 8 wefts. Warp = yarn that runs vertically Weft = yarn that runs horizontally Damask is usually formed of satin/sateen structure (or can be a twill), where the design appears to 'sit' on top of the fabric, and the pattern in reverse colours can be seen on the underside of the fabric. Hope that helps! It's hard not to get too techinical, unless you already have weaving knowledge?