It’s been some time since I wrote a Japanese language post, but when I first learned about なにげない and さりげない, I couldn’t grasp the difference immediately because the English word for both could be simply “nonchalant.” But there is stark difference in the actor in that, it depends on whether an action is deliberate or not; whether a specific knowledge in something plays a role in the action taken.
For lack of a better example, X received a souvenir from A who went traveling recently. X excitedly shares that with B, not knowing B is also going traveling soon. And then B said, “Actually, I’ll also be going traveling next week. I’ll get something for you too!” In this case, X なにげなく told B about the souvenir from A.
Now, picture the same situation that X received a souvenir from A who went traveling recently. This time, X knows about B’s travel plans and wants a souvenir from B, but without asking too directly. So X goes to tell B about having received a souvenir from A, so as to drop hints for B to get a souvenir for X. In this case, X さりげなく told B about the souvenir from A.