What is the difference between the A text and B text of Doctor Faustus?

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.