Damascene sometimes refers to patterns that arise within the steel.  The word itself means (more or less)  "from Damascus", a city where many fine weapons were crafted.  To learn more about these types of patterns, see the pages on Wootz and Pattern Welding, generically referred to as "Damascus steel".

Considered as a type of decoration that most commonly known as a decorative pattern as practiced today in Toledo, Spain, Damascene combines two metals not by forging but by soldering.  Inlay materials are invariably silver or gold.  This process is akin to Koftgiri and is also referred to as "cloisonné"

"True damascening" is an inlay technique wherein a soft material such as gold or silver is hammered into in a pattern carved into the underlying metal.  The grooves are dovetailed in shape.  When the inlay material is hammered into place, the sofer metel flares out to fill the groves and thus becomes securely attached to the underlying material. This process is known as "tab i nishan" in India and "honzogan" in Japan.  Sometimes the inlay metal is hammered flat, other times it is allowed to stand up in relief.  In Japan, if the inlay is flat it is called "hira-zogan" and if in relief, "taka-zogan".  Few other countries have specific names for the variations of true damascening.  

"False damscening", alse called "encrusting", is more of an overlay (onlay) technique where the underlying material is roughly scored and the decorative metal is then laid out in a pattern and hammered into place.  Although it looks good, it does not wear very well.

Generally, any protruding decorative material is burnished to be smooth with the adjacent surface.  If it is left to protrude, it is sometimes called "encrusting".

Both true and false damascening were used in Persia and India.  In North Africa and Malaysia only true damascening was used.  Damascening was seldom used in Europe where fire-gilding was the preferred method.

Here is a picture of a 19th C Ottoman Saber that shows all of these techniques.