You might think that the term woolen yarn has to do with yarn being made with wool, but actually woolen yarn in the spinning world refers to a particular way of preparing the fiber and a specific spinning technique that can be used on a variety of fibers.
In contrast to the worsted method of spinning, woolen fiber preparation isn't concerned with lining up all the fibers or making sure that the fibers are of the same length. When the fiber is spun in a woolen style, the twist is allowed in the drafting zone, meaning that the twist is worked into the fiber before it is thinned out of your fiber supply.
Woolen spinning is fast and a little wild and untamed; trying to control the yarn too much only results in trouble and a much slower process. Because the fibers aren't arranged before spinning, this yarn is much fluffier and warmer than a worsted yarn. It doesn't provide good stitch definiton because it tends to produce a halo around the stitches. It's not very strong, though plying can improve its strength.