What does the weapon icon mean in Total War Attila

In Attila (and in fact most recent Total War) every unit has a "weapon", often displayed in the unit's name. You can also see it in the form of a little icon on the unit card. For example, Axe infantry use Axes, Spearmen use spears (obviously).
Do these icons means something more than what is already displayed in the unit stats (like numerical values )? Do Swordsmen have any hidden bonuses over Spearmen, for example ? Or Axemen against infantry? Or Spearmen against cavalry ?
I looked in the game wiki but I found nothing specific about this.
Best Answer
As you've mentioned, the weapon icon indicates the type of unit.
I've found the following information relating to the strengths and weaknesses of the various types units in Atilla: Total War (and these should generally hold true for other Total War games as well). If I've missed any, feel free to edit or comment, and I'll try to add them.
Infantry
Strengths: Average Missile Block Chance, Formations, Prolonged Combat
Weaknesses: Flanking, Persistent Missile Damage, Sea Sickness, Shock Cavalry
Strengths: Average Missile Block Chance, Disciplined, Fighting Cavalry, Formations, Good Armor, Strong vs. Charges
Weaknesses: Flanking, Persistent Missile Damage, Prolonged Combat (vs Melee Infantry), Sea Sickness
Strengths: Disciplined, Fighting Cavalry, Good Morale, Pike Wall, Strong vs Charges
Weaknesses: Flanking, Persistent Missile Damage, Prolonged Combat, Sea Sickness
Missile Infantry (Archers)
Strengths: Barrage, Flaming Shot, Heavy Shot, High Persistent Damage, Precision Shot, Whistling Shot
Weaknesses: Cavalry, Flanking, Poor Melee Attributes, Poor Morale, Prolonged Combat, Sea Sickness
Cavalry
Strengths: Average Missile Block Chance, Diamond, Flanking, Good Charge, Good Morale, Strong Melee Attributes
Weaknesses: Aversion to Fire, Pike Infantry, Sharp Rock Beds, Shock Cavalry, Spear Infantry, Spike Traps, Suedes
Strengths: Barrage, Fire While Moving, Formations, Mobility, Precision Shot
Weaknesses: Aversion to Fire, Melee Cavalry, Persistent Missile Damage, Pike Infantry, Poor Missile Block Chance, Sea Sickness, Shock Cavalry, Spear Infantry
Strengths: Excellent Charge, Flanking, Good Armor, Good Health, Wedge
Weaknesses: Persistent Missile Damage, Pike Infantry, Prolonged Combat, Sea Sickness, Sharp Stone Beds, Spear Infantry, Spike Traps, Suedes
Strengths: Fire While Moving, Flaming Shot, Heavy Shot, Powerful Charge, Scare (everyone), Whistling Shot
Weaknesses: Aversion to Fire, Run Amok, Sea Sickness
Artillery
Strengths: Barrage, Excellent Missile Damage, Excellent Speed, Unit Penetration
Weaknesses: Cannot Run, Poor Melee, Poor Morale, Sea Sickness
Strengths: Barrage, Excellent Range, Explosive Shot, Flaming Shot, Siege Damage
Weaknesses: Melee Combat, Persistent Missile Damage, Poor Health, Poor Morale
Ships
Strengths: Barrage, Douse Fire, Excellent Range, Flaming Shot, Good Hull Strength
Weaknesses: Flammable Vessel, Poor Boarding Actions, Poor Morale
Strengths: Douse Fire, Good Mobility, Greek Fire
Weaknesses: Flammable Vessel, Poor Boarding Actions, Poor Morale
Strengths: Douse Fire, Good Hull Strength, Good Morale, Strong Boarding Actions
Weaknesses: Flammable Vessel, Persistent Missile Damage, Prolonged Combat (while ashore)
Strengths: Douse Fire, Flaming Shot, Good Rate of Fire, Heavy Shot, Replenish Ammo, Whistling Shot
Weaknesses: Flammable Vessel, Poor Boarding Actions, Poor Hull Strength
Strengths: Devastating Ram, Douse Fire, Excellent Hull Strength, Ramming Speed!
Weaknesses: Flammable Vessel, Poor Boarding Actions, Poor Morale
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Total War Attila Mechanics - Weapon Length and CA Plz
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