Will my "the finalist certificate of the best paper award" be underrated if I co-chair a session at the same conference? A paper of mine did recently reach the final competition for the best paper award of a prestigious conference in my field. Although mine didn't end up with the best paper award, yet I'd like to note that in the "honors and awards'' section of my CV because the conference is arguably one of the bests in my field, and even getting through the roster of its finalists means a lot.

On the other hand, I was also the co-chair of one of the sessions of the conference. I had neither any impact on the selection of the finalist nominations nor any vote on the overall award process whatsoever. Since I'm a rookie Ph.D. student, I'd also like to quote this role in the "academic experiences'' section of my CV (next to my reviewing roles, TAships, etc).

Now I'm wondering if I take both ideas above into account, one may think that my co-chair responsibility would have influenced on my finalist achievement. How would academicians interpret this case? Do I have to pick one to avoid such a misinterpretation?
I would propose to put both points into your CV.

The interpretation you're afraid of is a bit far-fetched, and while some persons may indeed come to such a conclusion, I think most will not. Even for those who would think there has been an influence, I would argue that putting both is better than putting only one of them.
This is because they are in different CV categories, and thus people who evaluate your CV will in their mental checklist tick off both "won a paper award" and "chaired a conference session".