The first one is slightly more ambiguous. I think that if I ask you buy me something, you pay for it. (I'm not sure who has the right to ask this of you outside of your family, but that's not the point.) But with the right context, it could be possible that there will be reimbursement.
If you want so suggest you'll pay for them, you can use the phrase "pick up some" -- that does have a sense that you will reimburse the person for the purchase. Least ambiguous of all, of course, is "If I give you a few dollars, could you grab some apples for me while you're there?"
With the second one (I bought him some apples) there is absolutely no sense that he has to pay for the apples. To the contrary, it sounds like a gift.