IB Math AI HL vs AA SLWatch
the difference between AI and AA courses is, as you said, AI focuses on practical uses of maths and AA on theory. essentially, this means that AA is more difficult for majority of people since it requires some abstract, logical and mathematical thinking, while AI doesn't (so much). so in AA you learn about functions, calculus, probability and (very little compared to AI) about statistics. AI is much more focused on statistics. in our school we have only AI SL and AA SL/HL, so majority of people who are going to go to humanities at university and/or are bad at maths chose AI SL.
you can have a look at the guides for both (they are surely available online) and make your decision.
PS. I'm doing AA SL so if you have any questions about this, let me know