Not at all. The distinction is very real. Many copyright infringement lawsuits are not about the money, but are about the use of copyrighted material in a way, or by an entity, that the copyright holder doesn't approve of. They aren't upset that they weren't getting paid, they're upset at their work being used in a way they oppose.

It's also true that (outside of criminal copyright infringement) the only remedy that a court can offer is monetary. But that fact doesn't mean that money was the real issue at hand.