Capture is granted by the Thief Glove. It adds a basic attack to Steal and has the same chance of success. The attack is made normally, but ignores most special abilities of the Weapon used. This can severely impact the effectiveness of the Weapon being used, so be careful with Capture. (The full list of Weapon effects can be found in the Game Systems document.)
Mug adds a chance to steal Items to a Character's normal attack. You can only successfully steal from a given enemy once, and if you do, they won't drop anything after combat. Different enemies have different resistances to Mug. The Character's Speed will increase the success rate of Mug.