If you ride Western, any bit with or without shanks and a jointed mouth piece may be called a snaffle. This could be a curb bit like the popular short shanked Tom Thumb or any other bit with or without leverage action. There are many types of bits that have specific names and some, even though they are really curb (leverage) bits, might be referred to as a snaffle bit.
A snaffle bit is never a leverage bit regardless of the type of mouthpiece it may have. Even bits like a Kimberwick are not snaffles since they are leverage bits even though they have very short 'shanks' and look very similar to an English snaffle. Snaffle bits do not have shanks, nor do they use leverage action. To call any sort of leverage bit a snaffle is erroneous.