The other reply is really good. To add to that, the intersection of two bi-cubic Bezier patches (each being but one part of a cubic B-spline surface) is an implicit equation of degree 18^2=324. This simply cannot be implemented exactly in a geometry kernel and thus must be approximated. How do you want to approximate this? If you choose trimming (the industry standard) now you have to handle gaps in your geometry. If you choose remapping into an unstructured watertight spline, you need to solve a constraint system that is NP-hard. If you choose reparameterizing… well, see nVariate’s watertight Boolean technique (disclaimer: I once sponsored a project with nVariate).

Now, generally speaking, in a CAD model most surfaces will be “analytic” (plane, torus, conical, arc, line, etc). But whenever some complex surface that joins these surfaces is required, (NUR)B-splines are the principal technique for “covering” the gap.