No Mazdaspeed badge on my '13 Club. The dash panel has an "MX5 ===========" racing stripe-like graphic on it. The dash is the same color as the car in my case, True Red. There is a Club badge on the upper front quarter panel behind the front wheels on both sides. "MX-5" graphic on the rocker panels below the doors on both sides that matches the smaller one on the dash.
The GT is the exact same car in all respects, save the Club badge and graphics. In addition, the GT usually has leather seats, not an option on the Club, which has cloth seats. GT usually has upgraded Bose sound, Bluetooth hands-free phone integration with steering wheel controls, and AKE. AKE might have been an option on Club, not sure. Mine has regular key.
The one in my avatar is my GT. If you want to examine my Club, come out to the bus lot on the 18th.