GT5's was called "Spec 2.0" and brought game version 2.0. That's all it brought, and that was the game's 13th update. And, crucially, "GT5 Spec 2.0" was only available in Japan.
As for the "host of new content", GT5's game version v2.00 actually brought:
A new opening movie
11 NASCAR stock cars
Nissan GT-R N24 Schulze Motor Sports '11
Mid-race saves
Simplified cockpits
Daily login bonus
It also enabled DLC compatibility, and the first of those - Kart Space, Spa ($5 course pack), the Touring Car pack ($8), paint pack ($2) and racing gear pack ($3) - arrived a week later and was not included in the GT5 Spec 2.0 box. Primarily what buying "Spec 2.0" did was save you having to download 13 updates, and added 12 cars, compared to the base game. And a new opening movie.
The US market "Gran Turismo 5 XL Edition" arrived almost three months later, and included vouchers for that DLC - and I think also for the later hot hatch car pack.
Last was the European (and Australian) equivalent. GT5 Academy Edition didn't arrive until nearly a year later, in September 2012, but included all the DLC up to the Speed Test pack, but not the Twin Ring Motegi pack which is odd as that came out in June 2012. I think that this is what you're thinking of when you say GT5's Spec II was "really a Spec II", but this wasn't GT5's Spec II. "Spec 2.0" was.
Meanwhile GT Sport Spec II saves you having to download 37 updates, and adds 125 cars and 36 tracks, compared to the base game. And a new opening movie.
Our only other "Spec II" was GT5 Prologue. That expanded the game from 37 to 71 cars, and added one track (High Speed Ring, forward and reverse). That came on a new disc in Japan, but it was also the first version of the game outside Japan. There was also a "Spec III" with all the updates released in Japan on a new disc.