Derating ampacity of a wire if it is stranded?
Gauge is defined by cross-sectional area, not outside dimension, so the stranded #12 wire has the same per-length resistance as the solid #12 wire. Ampacity is more complicated (it depends on type of insulation, what other wires are nearby, and other details), but whether it's solid or stranded again does not matter (or at least not significantly so) for this.

AC vs DC also has no impact, unless your "stranded" wire is actually litz wire. As litz wire is very expensive and has to be specially ordered, it almost certainly is not--you would know if you had it.