Mild Al, maybe I'm just not as mild as you since for the purposes of these forums I count any non-recreational riding I do on my bike as "commuting" and don't think twice about it. Though, strictly speaking, I suppose "commuting" is defined by the ride from home to work and the reverse. I, for one, do not limit myself here to that definition. My looser definition might be "going to and fro in the engagement of personal or professional business". I even extend my definition to rides that might otherwise be termed "recreational"- like long rides I take to visit family or friends. I ride to work pretty much everyday, to ride to the grocery store, the movies etc. but I call all of that "commuting".

I seldom drive my car and seldom drive for "recreational" purposes despite the "pleasure roads and highways" built in the 1950's the concept of the "sunday drive" is pretty antiquated for everyone but I certainly do take pleasure rides on my bike and those I do not refer to as "commuting".

I have a cabin in the mountains that I go on weekends. So my travel back and forth there is commuting. Therefore, for the times when I ride my bike to get there, I guess that counts as bike commuting.

On the other hand, I travel back and forth from the grocery store once a week, but no one would call that commuting?

I count those commutes as "pleasurable commutes"!

oh, oh... count me as one that would. Does that make me "no one"?

I don't think any of the things mentioned in the original post matter. I do think you need to do it more than once to be a commuter. Maybe at least once every couple weeks.

Like any word, commuter means what the people who use it want it to mean. I suspect it was coined when urbanites first started to move to suburbia in big numbers in the 1950s, to refer to what was then the novel practise of travelling a long way to work every day. So someone who still lived in an inner city neighbourhood was simply "going to work" while someone who travelled a long way in by car or train was "commuting". Over time that notion that commuting has to involve a long distance has faded, and now the word refers anybody on their way to work, and apparently can refer to people going on other errands. Still, the dictionary definitions online suggest that commuting implies a regular, repetitive action.

"On the other hand, I travel back and forth from the grocery store once a week, but no one would call that commuting?"

Any time that I ride my bike for a chore or task I would otherwise take my car it is commuting to me.
Any time I ride for fitness with no specific chore or task in mind it is exercise.

Today I had an onsite client meeting so I had to drive to work and then to their location. I then drove back to my house had lunch and rode my bike into the office to finish my day. Tomorrow I'll just ride in and not drive.

I still call my self a bike commuter. Just ride and enjoy! Anytime you ride instead of drive you help yourself, your wallet and the environment.