Counted-thread embroidery is any embroidery in which the number of warp and weft yarns in a fabric are methodically counted for each stitch, resulting in uniform-length stitches and a precise, uniform embroidery pattern. Even-weave fabric is typically used, producing a symmetrical image, as both warp and weft yarns are evenly spaced.
The opposite of counted-thread embroidery is free embroidery.
Cross-stitch is a form of sewing and a popular form of counted-thread embroidery in which X-shaped stitches (called cross stitches) in a tiled, raster-like pattern are used to form a picture. The stitcher counts the threads on a piece of evenweave fabric (such as linen) in each direction so that the stitches are of uniform size and appearance. This form of cross-stitch is also called counted cross-stitch in order to distinguish it from other forms of cross-stitch. Sometimes cross-stitch is done on designs printed on the fabric (stamped cross-stitch); the stitcher simply stitches over the printed pattern. Cross-stitch is often executed on easily countable fabric called aida cloth, whose weave creates a plainly visible grid of squares with holes for the needle at each corner.
Fabrics used in cross-stitch include linen, aida cloth, and mixed-content fabrics called 'evenweave' such as jobelan. All cross-stitch fabrics are technically "evenweave" as the term refers to the fact that the fabric is woven to make sure that there are the same number of threads per inch in both the warp and the weft (i.e. vertically and horizontally). Fabrics are categorized by threads per inch (referred to as 'count'), which can range from 11 to 40 count.
Drawn thread work is one of the earliest forms of open work embroidery, and has been worked throughout Europe. Originally it was often used for ecclesiastical items and to ornament shrouds. It is a form of counted-thread embroidery based on removing threads from the warp and/or the weft of a piece of even-weave fabric. The remaining threads are grouped or bundled together into a variety of patterns. The more elaborate styles of drawn thread work use a variety of other stitches and techniques, but the drawn thread parts are their most distinctive element. It is also grouped with whitework embroidery because it was traditionally done in white thread on white fabric and is often combined with other whitework techniques.
View the full Wikipedia page for Drawn thread work