Both wootz steel and pattern-welded steel are called "Damascus steel", but despite the superficial decorative features they are quite different. Pattern-welded steel uses the technique of lamination.
Unlike wootz steel, whose pattern arises from the presence of one or more impurities, pattern welded steel is the deliberate combination of billets made from different metals (iron alloys) during the making of a blade. The esthetic result is similar: waves and circular patterns of light and dark steel.
Pattern welded steel is made using a similar technique to laminating or piled steel. Two or more metals of different combinations are heated to a very high temperature and then hammered together.
The need for these techniques come from the competing requirements of a good sword: It must be hard and durable (hold a keen edge) yet must also be somewhat flexible to avoid breaking during combat. The technique also arose by necessity: early foundaries could not produce steel with consistent quality. Bladesmiths had to work with a variety of steels available from different sources, and only by combining them were they able to "average out" the differences and achieve the desired qualities in their own product.
Pattern welding is known to have existed as early as 500 BCE as it is found in some Celtic swords from that era.
High carbon steel was the most difficult to make and most expensive to acquire. One way to conserve the amount used was to limit it to certain parts of the blade where its properties were most useful, e.g., the edge of a blade, or strips within the core. Two layers of softer steel would be placed around a high carbon steel strip. It was not uncommon to have swords with five sections of differing properties due to the various steels welded together.
Patterns may be built up from multiple rods composed of different steels welded together. The rods could be twisted left or right, or alternativing (making a chevron pattern). Flattening and hammering and other mechanical manipulations could be used to achieve even more complex patterns. A skillful smith pounding an ingot with different force and direction can create these patterns. The patterns can be distorted through careful chizeling of grooves into the blade, distorting the existing structure. The famous “40 steps” pattern ("Mohammad's Ladder”, "Kirk Narduban) is an example of these techniques.
As with wootz, the pattern is revealed through a careful acid etching process that has a different effect on the steels used in the blade.
While twisted welded steel has technical advantages compared to forged welded untwisted rods, it also yields beautiful patterns that were created for their own sake. Sometimes smiths would simply adorn a homogenous steel place with a decorative thin layer of pattern-welded foil.
The beautiful patterns known as "pamor" found in blades from the Indonesian Archipelago is a result of alternating layers of steel and iron containing nickel (nickel alloys). The contrasting layers are folded, twisted, threaded through holes and undergo various other mechanical manipulations during forging. The result are the hundreds (or more) patterns found today, each with its own name and special meaning.
For an excellent tutorial on pattern welding, see http://www.cashenblades.com/damascus.html