the number of coordinates collected per unit area
Where did you find this definition? (it looks like a typo ;).
Bascially, when you define a 'radius', we count the points that fall inside the corresponding sphere. So you either derive from this:
- the volume density, which is the number of points divided by the sphere volume
- or the surface density, which is the number of points divided by the disc volume (assuming the surface is locally more or less flat)
And yes, it generally makes more sense to use the surface density.
Last, the Align tool is not iterative contrarily to ICP. It just registers the set of points you've selected in one shot. And that algorithm is actually the same as the one used by ICP for a single iteration (see "Closed-form solution of absolute orientation using unit quaternions" by B. Horn).