difference between iphone5s factory unlocked and internationally unlocked?

hey guys.

i bought iphone5s yesterday from apple store at 5th avenue. and the sales agent said to me that they dont carry factory unlocked iphone 5s but they do carry internationally unlocked iphone5s. i am confused! i want to use this phone in canada. so will it work on any carrier in canada as a unlocked phone?? they said to me that when i will come back in U.S with that phone , it will act as a locked iphone and will only work on at&t network. so my question is, is it still unlocked iphone even though i paid $706.06 and will it work in other countries if i use any sim.