Basically, they are just two different versions of the same play.
The 'A' text survives in two printed versions: a 1604 quarto (reprinted in 1609) which attributes the play to 'Ch.Marl', and, at 1485 lines long, is one of the shortest Elizabethan plays in existence.
The 'B' text is a 1616 quarto reprinted several times, and is substantially bigger than the 'A' text, adding around 650 lines.
Scholars still argue about the relationship between the two different versions of the play (and whether either or both plays represent the unedited work of Marlowe) - and so modern editions most usually print both, as is usually the case with a book just called 'Dr. Faustus'.
I'm sure the OU should have given you a more detailed reading list: if they specify a certain edition to buy, you could work out by searching it on Google Books which text is the one they want to study. But if I had to bet, I'd say it'll be the 'B' text you want.
I am just starting with the Open University, and they have asked me to get the A text.
There are a lot of differences between the two texts. One of the main differences is the language. The language in the B text has changed quite a bit. In the B text certain parts have been deleted and seven hundred plus lines added. In addition, some of the scenes have been reorganized for consistency. There is a Norton Critical Addition of Doctor Faustus that has both texts and a few essays that outline the main differences. If you are looking to write a paper on this play I would suggest going with the B text but that would entirely depend on what your paper focus will be. I posted a link that allows you to look at the differences of the texts on line. I hope some of this helped. I know it is not very specific but if I were to list all of the differences we would be here a really long time.