Oh, this one's not too hard, so I might be of some help here, even though I'm not a teacher.
Apparently the 'A', which makes clear(er) that both abbreviations stand for the United States (of America).What is the difference between U.S. and U.S.A?
It really makes no difference, unless you'd like to make sure, that everyone is aware you're speaking about America -- and not about any other "United States".When do one use US and when do one use USA
In America, they mostly drop the 'A', as is it is obvious which states are meant. But elsewhere this is quite similar. U.S.A. is just more complete and practically always used in formal instances, as for example printed on commercial products: "Made in USA"