Tactical mastery increases damage done by 'spells' and heals (mostly rune-keeper, lore-master and minstrel). Physical mastery increases damage done by melee and bow attacks for the other classes. There is some cross-over, for example, minstrels will exclusively want tactical mastery for their heals and cry-based attacks but the physical mastery rating will also give them a damage increase on the limited melee attacks they have. Likewise captains need physical mastery for their melee attacks, but tactical mastery increases the magnitude of their heals.
Finesse reduces the chance for physical (melee and bow attacks) to be block parried or evaded by your foes and also reduces the chance for tactical attacks (spells, crys, taunts etc.) to be resisted