There's no substantial difference between those two methods.
Affinity Map Sessions have two main goals:
- Generate discussion.
- Organise Content.
Card Sorting Sessions have one main goal:
While discussions do naturally occur during Card Sorting sessions, and you can even take notes on that, it's NOT their main purpose.
So, we end up using Affinity Map sessions with internal teams more often, due to the discuss element of it, and Card Sorting more with the users.
BUT, nothing stops you to use Affinity Map sessions with the users.
At the end, what to choose?
Evaluate your users, do you think you will get useful information allowing them a more open to discussing session? Go with Affinity Maps.
Are they introvert? Hard to think out loud? Go with Card Sorting.
Bottom line, they have nuances, but they have the same goal at end.
There's someone who can explain it, much better than me:
So, you know, at the core they’re the same because they’re about
getting little pieces of stuff and assembling them into bigger. The
difference is with a card sort…and they’ve just come out of history in
different ways… in a card sort I would do that with external people or
people who will be users of the site, in an affinity diagramming
session I would tend to use that with my design team.