B-Spline Surface Case:

This case illustrated two B-spline surfaces with the same underlying control mesh. The first is a biquadric (i.e., p = q = 2), whereas the second is biquartic (n = p = 4). The U and V vectors are consistent (the only interior knot in each of case is at 0.5).

Note how the lower degree surface is much closer to the control mesh, whereas the higher degree surface is much "smoother".

B-Spline Surface Case

The surface is constantly differentiable if the underlying B-spline curves are in the interior of a knot span, the surface shall be constantly differentiable arbitrary number of times. What regarding the partial derivatives at a knot? For a knot of multiplicity k, the surface is (partially) differentiable (p - k) times w. r. t. u, and (q - k) times with respect to v.