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.
Strangely, the industry doesn't seem to find it confusing at all, despite the best efforts of the manufacturers to bamboozle us.
Given that all commercial aircraft types are certificated, the Type Certificate is a pretty good place to start when trying to differentiate between what is a different type and what is merely a variant.
So, for example, none of the Boeings listed share the same TC, nor do the A330/A340, but the A318/A319/A320/A321 do.