This gets asked frequently. I think the actual definition is an oft-repeated trip. Grocery store counts. But... I only count work commute miles in the commuting mileage thread.

Dictionary.com says "to travel regularly over some distance, as from a suburb into a city and back: He commutes to work by train."

In this case, "commuting to work" is an example, not the hard definition. You can commute other places besides work.