Yes the T2 was the sports car varient and it climbed higher up to about 42,000 feet...The T3 was limited to 35,000 feet and had no "Drop Down" passenger oxygen system. The plastic Boost Engine had 5500 lbs of thrust and you used it for take-off if the runway length or air temperature were limiting. You could also light it in the air if extra thrust was required if you had lost a main engine.
I did lots of Warsaws on the T3 and it was always very full...Often with no seats left at all.
The sideways retracting nosewheel saved an enormous amount of space to put the electronics bay in.