Unlocking weapons for all classes occur horizontally on the weapon-list grid, and can transfer across classes so long as the weapon set is identical for both classes. Thus, a War Axe kill as the Vanguard will count towards kills on the Man-at-Arm's primary axe weapon line, and so forth. The only exception is the Vanguard's shortsword line, which appears to share unlocks with daggers.
All weapons and items wielded are designed to kill, thus do heed caution when attacking. Do watch out for friendly-fire. This is particularly dangerous when ganging up with an ally to kill enemies, as one careless hit could prove fatal to both your friend and the outcome of the battle.