There are now three broad sectors of the economy: public, private, and 'third sector'. The latter includes charities, non-profit-making organisations, social enterprises and even universities now that they have to raise their own funds. Many such entities are constituted companies/corporations, and make a profit in the sense of having greater income than costs, but they don't distribute that profit to shareholders or owners but plough it back into the company and its works.
Which is going a bit 'meta' on your question, I know, but is relevant. If a social enterprise, say, sells a CC-licenced product at a profit, does that count as commercial use? My personal feeling, having produced a lot of OER, is 'no', but I can see that it would count as a 'grey area'.