If we're talking about the United States, it's not an oxymoron at all. I've got some extremely profitable 501(c)(3) non-profit organizations I could show you. Autism Speaks comes to mind. They may not be making money for public shareholders, but they're making a lot of money for the people who run them, all the same.

Also plenty of organizations look like businesses in every way except their tax status. Thrift stores, for example. Goodwill isn't a nonprofit anymore, but even when it was it also employed all the same abusive labor practices and suchlike that you'd expect from a for-profit business.