Counted cross-stitch designs are not printed on the cloth. Those are stamped designs.
Counted cross stitch patterns come with a chart that indicates which thread to use by which symbol is printed. Counted cross stitch is generally done on an evenly woven fabric, like Aida, linen, evenweave, etc. You count across the appropriate number of threads on the cloth to place each stitch. They are able to be more complex, generally, than stamped cross stitch because you are doing the work of counting where the stitches go (and in most cases, the stitches are smaller).
Some counted cross stitch projects include other embroidery stitches, most often backstitching and/or french knots. Occasionally you'll run into lazy daisy stitches. Most do not (At least, I've never run across any that do) use stem stitch, and only rarely use satin stitch - I've only seen it once. If you want to know what stitches are in a specific design, ask on the forum and Kristi - who works for ECS - can usually let you know pretty quickly.
I do both counted and stamped projects and both can be lovely, but I prefer counted generally because the designs are more interesting to me and fun to do.