Spoken like a true tungsten connoisseur.

Drill bits are coated in tungsten carbide. Sometimes. There are a variety of coatings.

The drill bits you're buying at the big box store are high speed still with some kind of coating to help them last a little longer. The specialty drill bits you're buying for working on metal are also HSS with a different coating and probably different tip geometry.

End mills are milling/lathe inserts can be HSS or carbide, also with some tungsten coating. Importantly, these are sintered, and made out of dust.

Tungsten carbide is waaaay too brittle to work as a drill bit.