I am not sure, but I think normally "check card" = "debit card" = "ATM card". They all directly deduct money from your account (usually a checking account) at the time when you use the card.

If the card has a "Visa" or "Master" logo on it, then it can be used at any place where "Visa" and "Master" are accepted.

I am not sure what BOA has to do with 建行. However, I think you can not withdraw US$ directly in ATMs in China. (否则建行的ATM中要准备多少种钞票呀?)