Clinchers are where the tire is open on the inside, a tube goes inside it, and it clings to a kind of hook on the rim on each side. Tubulars are fully enclosed with the tube already inside, and are glued to a rim that has no hook.

Zipp 404 would be a huge upgrade, although I would personally not run carbon tubulars for daily riding. They would be racing only for, but there are those with different opinions. Tubulars are a little trickier to fix flats mid-ride, although they seem to flat less... and you can continue to ride (gently) on a flat tubular tire if you had to.