It's a good question, and to be fair there is a broad range of things that go on under that label.
I would draw the distinction between freelancing and consulting this way: you are freelancing if you directly or indirectly (e.g. through a body shop consulting agency) are providing variable bandwidth for a client. So they could probably do the work themselves but need more horsepower. By comparison consulting would be where they bring you in to provide insight, experience, or skills they do not possess.
not the earlier parent, but ... I read it to mean self-employed. I 'consult', although probably at least 60% of the time it's just ... code/development. But with the experience I have, some clients engage me to be more than a pair of hands, and there can be 'consultative' engagements: helping develop plans, strategic guidance, etc.
But it can also mean working for a larger agency, focusing on specific areas (of technology, or industry, etc). To me 'consulting' has some connotation with 'deep expertise' in one or more fields.
