I'm thinking there isn't much difference between the two, but the impression I get is some think that "biking" is what Hell's Angels do, and "cycling" refers to those of us who pedal...
I know I feel a wee bit smug when I pass a runner, like I have some magical wings, and feel sorry for the thousands of bones in his/her feet, pounding the pavement. When a Biker (motorized) goes flying by me I feel a bit envious, but still smug, like "Hey, I'm working out, what are you doing?!" Of course they smirk back at me like "So slow!"
But "cycling" means servers to me - not waitresses (oops that's not PC is it, like "stewardess" is now "flight attendant" - should be "server"), but computer servers. They get cycled and so do lots of other things. I never think of cycling my bike, I just ride the darn thing.
Speaking of which I got lost on Saturday on a 25 mile ride. I was a bit miffed about it, with ground support (Tom) being kinda slack and giving me directions like "North on Sksjfadfh", instead of "Right in .5 miles on ______" (I was hoping for an intelligible street name). Something about heat and hills and sweat and exhaust furmes can fry your sense of direction and sense of hearing. There should be a study.
Then I realized, what the heck, I don't know where I am, but that happens all the time anyway. There's no such thing as a bad bike ride!
Last year I rode in a tsunami and it was great. Flooded so bad we had to stop, and it was terrifying and glorious. Nothing like riding in a summer storm with lightening to get your sense of awe in order.
so cycling and biking, I do both. No more servers, but lots of going round and round, sometimes with my arms wide open in the rain, spinning.
v