In a lot of examples, commutivity is obvious:
- The two computers can easily swap data.
- We swapped houses during the children's school vacation.
- Do you want to swap places?
- If you prefer to sit next to Chris, I'll swap seats with you.
- When you've finished reading your book, and I've finished mine, can we swap?
- We swapped addresses with the people we met on vacation.
- We spent the evening swapping (= telling each other) stories/jokes.
But the non-commutative sense may be the default as in this specifying definition (in the examples given, it is contextually forced)
swap someting for something: to exchange something you have [or in hypothetical situations would see yourselves having] for something else:
- Most consumers said they wouldn't swap the product [they owned / desired] for a cheaper own-label brand.
- They've swapped their old car for a much larger one.
- When he got a job in a bank, he had to swap his jeans and T-shirt for a suit (= he had to wear formal clothes instead of informal ones).
- [ + two objects ] I'll swap you my chocolate bar for your peanuts.
(All quotes so far from Cambridge Dictionary, re-ordered.)
But as I expected, counterexamples aren't hard to find on the internet:
- "I'll swap you your pasta salad, for this apple", my friend would tell me.
- I'll swap your flat mate for mine ..."
ie 'I'll / I would exchange something else for something I have.'
So 'I'll swap A for B' does not entail that it is A or B that you have. You have (perhaps hypothetically) one of them. Directionality (who is the donor and who the recipient) must be indicated by context, though A is more usually owned by the speaker.