1862 S Seated Half For Your Consideration.

I'll say AU-58 , she's a good looking coin, and from the pictures provided it looks like you have:

WB-4, "Bearded Liberty," Medium S, Damaged 6, with a rarity of R3.

Is that a surface stain or corrosion?

Whoa, I'd come in a lot lower. My first thought was VF-35, with lots of wear over Liberty's head, thigh, shield, and stars. Obverse rim is very weak which I suppose might be partially due to strike weakness. The reverse is better but shows wear over eagle talons, legs, and wing edges as well as arrow feathers and olive leaves. The small rim ding at 2:00 on the obverse doesn't qualify as damage. The stain hurts eye appeal but doesn't look like corrosion.

An AU coin should have remaining luster in protected areas but I don't see any. I might stretch to XF-40 overall if the rim weakness can be attributed to a striking problem.