What is the difference between "coming" or "going" and "heading" somewhere?

I don't think this question is frivolous. "Come" and "go" sound more imperative. "Head" has more of a "mosey at your own pace" connotation.

To head somewhere generally denotes to start moving, as opposed to 'go'. 'Head' is generally used with a direction; 'go' is generally used with a destination. Notice the difference:

We could go to the bar.

We could head towards the bar.

This is not a strict grammatical difference. It's just the way these words are generally used. 'We could head to the bar' is equally acceptable, but, like I said, the 'to' there is meant to denote a direction.