If this is how plastic is called in korea then why do I get boggled looks when I say 플라스틱 가방 to clerks and cashiers?
Because you are trying to translate "plastic bag" directly. It is not given they use those kind of words. I think 봉지 would be correct.
Because they distinguish between plastic and vinyl. I've heard 비닐백 but it isn't very common I think. Mostly the word 봉투 is used.
If you buy something in a shop the cashier will often ask "봉투 드릴까요?"