Indeed. There's only one musical activity I do for just the fun, and that's with lots of people doing things I'd not normally get the chance to do. Otherwise, show me the money: it's my job.
For me, if I'm doing am-dram - that's for fun. If you want me to accompany you or play the piano for something - that's work and involves £.
As you say - ideally I enjoy doing it while I am being paid, but work's work.
I was in a rock and pop covers band for a while, but our point of dissension was that the chap whose band it was and the bass player were both retired and whilst they would book gigs at pubs etc would never push for the money we should have been paid or charge if we were asked to play longer. The lead guitarist and I who are both semi-pro kept trying to push the idea that if you are booked to play from 9pm to 11pm for £200 and the pub asks you to play till 11:30 you say "yes, no problem - are you happy to pay an extra £50?". Also, the band should not have to buy their own drinks (within reason, but as all of us were usually driving, that means two soft drinks during the evening).