So, extracting value that doesn't belong to you, causing financial harm, but not physical harm. Sounds a lot like theft. If you walk into a bank with phony checks and walk out with money that isn't yours, how is that worse than walking in with a gun or sneaking in at night?
Sure, but theft is a subset of the crime in this case. Counterfeiting is a form of theft that literally destabilizes a regime. As jessaustin pointed out far more eloquently, my view is not novel. The fact that we have an organization within our government (the Secret Service) with a primary mandate of "defending the currency" should be enough for you to connect the dots and realize the counterfeiting is more than theft in the context of a nation.
* Steal a radio, you're stealing from a person.
* Run a Ponzi scheme, you're stealing from a group of people.
* Counterfeit a nation's currency, you are stealing from the people of that country.
So, to answer your question: Sure, counterfeiting is just theft.
We all agree that counterfeiting is a serious problem, so of course there is a governmental agency that covers "Financial Crimes, covering missions such as prevention and investigation of counterfeiting of U.S. currency and U.S. treasury securities, and investigation of major fraud" (according to Wikipedia).
I think you got to the heart of the matter when you wrote "Scale matters". Murdering millions of people is a bigger deal than murdering one person. Theft of millions of dollars is worse than theft of one dollar. The problem I have is the distinction is made not based on scale but by the means of theft. I suppose the idea is that is is worse to steal one dollar each from a million people than a million dollars from one person, but I disagree with that conclusion.