The two terms reflect different segments of the market though. You'd be hard pressed to find a freelance Management Consultant willing to self-identity as a gig economy worker.

That's true, but if you were at conferences for SuccessFactors or Workday about 4 years ago, you'd have heard lots of presentations about the rise of contingent workforce and the gig economy. In fairness to management consultants, most of them are not "contingent labor". Most of them are employed by companies. I think the major distinction is that "gig economy" tends to reflect contracting individuals only, while contingent labor includes both gig workers and those who are contracting through some kind of corporate entity like an LLC.