Fighting mode determines which Skill(s) melee combat Experience will be applied to. It also may temporarily change your modified /stats (located above game icons at top right of screen) associated with that skill by one while the mode is active as shown below. Fighting mode also determines where rewards exp is distributed i.e. Daily Rewards, Party Quests, Kill Quests and Towers room bonus. Archery will gain Towers room bonus if an arrow kills the mob.

Fighting Mode Experience gained by Melee damage Adjusted Pet
Accuracy Strength Defense Health Skill Bonus Exp
Controlled 2/3 x damage 2/3 x damage 2/3 x damage 1 x damage None 3 x damage
Accurate 2 x damage 0 0 1 x damage +1 to Acc 3 x damage
Aggressive 0 2 x damage 0 1 x damage +1 to Str 3 x damage
Defensive 0 0 2 x damage 1 x damage +1 to Def 3 x damage
Cordial 0 0 0 2 x damage -1 to Str/Def/Acc 2 x damage

There is no way to increase Magic skill with damage dealt with your weapon. Magic exp is gained by the casting of spells or by using Teleport Scrolls at 1% x /wiki cost (Dorpat Scroll costs 1000 coins and gives you 10 Magic exp per use) or Teleport Book. Memory Potions (Uniques) do not add Magic exp.

Archery gains exp from the damage done by arrows at 2x damage and does not add to Health.