Inventing means designing (described by regular COFES participant, David Ullman, P.E., Ph.D., and CEO as "the elaboration of information punctuated by decision).

Innovating means helping others appreciate and leverage your design.

As a VP at 3M noted, Invention turns money into ideas. Innovation turns ideas into money.

Our understanding of the fundamentals of both has increased considerably in this decade through research on how we think, c.f., "The Way We Think: Conceptual Blending and the Mind's Hidden Complexities" by Gilles Fauconnier and Mark Turner. 

Now we can harness the advances in digital electronics, software and social dynamics to take design to the next level. Challenges of extent, variety and ambiguity needn't bother us any more.