These are examples of low and high level armor sets available on the character creation menu. The examples shown do not reflect the only type of armor a class can wear. All races/classes can wear any type of armor.
Argonian
Dragonknight
Novice
Veteran
Nightblade
Novice
Veteran
Sorcerer
Novice
Veteran
Templar
Novice
Veteran
Dark Elf
Dragonknight
Novice
Veteran
Nightblade
Novice
Veteran
Sorcerer
Novice
Veteran
Templar
Novice
Veteran
Nord
Dragonknight
Novice
Veteran
Nightblade
Novice
Veteran
Sorcerer
Novice
Veteran
Templar
Novice
Veteran
Is this post-patch armour? Because I’m an argonian Dragonknight but my heavy armour looks just like that of the templar
This is what the Character Creation armor sets looked like at launch. Your class has absolutely nothing to do with how your armor looks. Armor changes based on level, material and quality and will look the same on every class.