To clarify, let's just say that soundcards were originally that... cards, or better yet, expansion cards since these were circuit boards installed in the expansion slots of computers. Audio interface is the all encompassing term for devices that serve as input/output devices for audio.
So, whenever we are referring to soundcards, you can be sure that these are expansion boards that reside inside a computer, while usb and firewire audio devices can be referred to as audio interfaces.