In a short nut shell.
The GT40 was designed by Lola in 59 (as I recall). Ford England bought the project after Enzo pissed off Henery. The car went through MAJOR changes by Ford, fitted with a small block and called a Ford GT MK1.
It was found that a big block would be much better for the long straight at Le Mans (Fords real target) so the MK1's chassis and body were modified to take a 427 Nascar motor and called the MKII, winning in 66'. This is probably the car you sat in.
It was toy with making the GT a street car to compete with the Vet, so a few MKIII's were produced. The nose and rear were both changed (DOT headlights and a trunk) but the car never went into production.
After 66' another GT40 was produced called the GT40 MKIV. This GT40 was a ground up design by Ford USA and except for the 427 Nascar motor shared nothing with the MKI, II or III's. It also looked VERY different and won in 67'.
When Ford quit in 67' the MKI was chosen by privateers instead of the MKII mainly because the 427 was outlawed, a ton of private R&D had already been done to the MKI and there were more MKIs available. Two of these cars became the famous GULF MKI cars winning both in 68' & 69'. This is the car (MKIs) ours was styled after.
On a side note, although Ford was officially out of endurancing racing in after 67' it is rumored that major back door factory support in the form of engineering and wind tunnel data was given to the privateers.
Steve