No. Tungsten is an element, where as tungsten carbide is an alloy, or a mixture of elements (tungsten, nickel, tantalum, niobium, titanium, and chromium). Tungsten carbide is much easier to work into styles and designs, but does not change the hardness of the metal.

You can find tungsten carbide mostly in the pen nib...

mold for tungsten carbide

Tungsten Carbide is made from compounds of Tungsten and Carbon. At the base level, Tungsten Carbide resembles a type of fine dark powder. This powder then made into shapes by being pressed.

"Carbide" as used in "Carbide Drills" and "Carbide Saws" is the alloy Tungsten Carbide. Chemically the material is either Tungsten Carbide (WC) or Tungsten diCarbide (WC2). Carbide is used because of its hardness.