Hey, Freaky,
Why do you think they call me KNOTHEAD?!? (Er, wait a minute...I call me Knothead...that is...Knothead is what I call ME...oh, dear, this isn't working at all..oh, well.

)
Seriously, though, a
Faucet is just the spout the water comes out of. The
Valve Stems are what the handles go onto, which turns the water on and off. A combination of the two would called a
Faucet fixture or Lav Set.
Perhaps THAT'S where my confusion came from
I just got done rebuilding the plumbing in my daughter's bathroom, and the zesty thrill of it remains a week later...

It's a double-sink setup, and the faucet and valve stems are separate units.
Oh, and Samwichse,
If you haven't done so already, be sure to replace the supply lines to the valves stems. They're not expensive, and new ones are cheap insurance against water damage.