Wrestling
Defaults: None.
This skill represents training at grappling and pinning. Roll against the higher of DX or Wrestling to hit with a grapple, or to make or resist a takedown. Furthermore, if you know Wrestling at DX+1 level, add +1 to ST for the purpose of making or resisting any choke, grapple, neck snap, takedown, or pin, and whenever you attempt to break free. Add +2 to ST for Wrestling at DX+2 or better.
When you defend with bare hands, Wrestling allows you to parry once per turn. You must use both hands. Your Parry score is (skill/2) + 3, rounded down. This parry is at -3 vs. weapons. For complete rules for parrying barehanded, see Parrying Unarmed.
Martial Arts
This skill is part of any style that teaches grapples, pins, and takedowns – many of which don't have "wrestling" in their name (see Wrestling). It represents a combat skill, not a sport, and offers defaults to many damaging techniques for knocking down or crippling foes:
Backbreaker, Drop Kick, Elbow Drop, Knee Drop, Piledriver, and Wrench Spine. These feats of strength nicely complement the Sweeps and throws of Judo. Fighters who know one skill would certainly benefit from the other.
Wrestling and Sumo Wrestling differ, too. Wrestling can't substitute for DX in a shove or a slam – and doesn't include sweeps – but makes up for this by giving a ST bonus that extends to chokes, locks, neck snaps, pins, and wrenches (unlike that of Sumo Wrestling). A fighter with both skills could slam or sweep a foe to the ground and follow up with a pin...or an elbow drop!
Like the bonus for Sumo Wrestling, Wrestling's ST bonus becomes a damage bonus when making an attack that inflicts damage: +1 per die at DX+1, increasing to +2 at DX+2 or better. The ST and damage bonuses for these skills never "stack." You only receive the bonus of the skill you're using.