Well if it's all about variants then the B707, B720, B727, B737 & B757, all Mk's of each, may be considered the same type as they all use(d) the same design of fuselage yet each merely had different attachments fitted to them!
Just because, for marketing purposes, the manufacturers designated these as different types doesn't change the fact that they are all variants of the same original design.
So what's the difference between an A330 and an A340, I'd suggest they are two variants of the same type ... oh, but if it's down to the number of engines then a Trident Three cannot be considered the same type as, or indeed a variant of, a Trident One or Two.