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.
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.