@Ash The elliptical shape superimposed on a T neck and top is what I traditionally think of with BT. Different sizes based on 1/8" as usual, commonly BT28, BT37, and BT56, but BT15 also exists and was used for some halogens, I am sure you have seen all of these.
That more cylindrical version common to 100/175W MV lamps is usually BT28 size, but I have also seen some rarer BT28s that look more normal, without sharp corners. Looking up "BT28 lamp" yields photos of both types of BT28 envelope. I personally am not huge fan of the less rare more cylindrical version that you are talking about, but it technically is still BT shape.
I have seen those tubular bulbs with only very small bulges with the HQI-BTs, I haven't seen any standard for that size. I haven't seen them referred as "BT##", just plain "BT". Unsure about the specifics there.