The double cut finish is executed by bead blasting the blade with ceramic/glass beads which essentially leaves very tiny pits on the blade surface. This gives a smooth, flat gray finish which is non-reflective, as chickenplucker said.

The satin finish is executed either by a high grit belt sander or scotchbrite pad abraded finish. The result is a smooth but more polished (and reflective) finish that is vertically oriented (on Busse family knives anyway) from top to bottom on the blade.

I agree with CP, both look very nice.