I don't agree with your definition. Commuting is just going from one place to another for a purpose. Nobody says you can't enjoy it too.
There have been precious few times when I didn't enjoy my ride. I will grant that I love it on the occasions when it's about 80 degrees, sunny and with a nice tailwind, but I'm having fun even when it's 0*F and I'm riding into a 20 MPH headwind that's driving wet sleet into my face.
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Work: the 8 hours that separates bike rides.