The US Stig is the same Stig as the British Stig.Someone was going to suggest it eventually, so we might as well just get it out of the way at the beginning.
The US Stig is the British Stig's other American cousin.Well, he can't very well be the first American cousin, can he? They look nothing alike.
Tanner is The Stig.There's an obvious bit of cost-cutting in the Stig segments (no music), the way his helmet lines up with his shoulders resembles Tanner and Tanner describes Stig laps in extensive detail that nobody on the UK show manages.
There will be a crossover between the British and US versions of the show in the near future.Hell, the British version has already crossed over with the Australian version and the German equivalent. It's logical that they'd cross the pond eventually.