Perhaps, Kasparov and Karpov's fire and ice styles fit with their Rebel and Collaborator reputation away from the board. Also Fischer was quite an aggressive person and player. Myself I am a positional player - I have no idea what that says for me.
Chess and personality
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Yes, there are definitely moves when you can tell some aspect of one's personality by how they're played.
For example, if your opponent has limited mobility in a closed game, patient people will take their time and maximize their position before attacking.
I think that those that bow to destiny, to "luck", those that are akin to gambling (dice lottery and cassino games) will prefer "blitz chess" just for the pure sake "of playing and see who wins (not to say anything about betting money)
Those that enjoy reasoning, observation, thinking,... that are tranquil, that do not rush to do things, that do not "vade retro" when a problem comes up, are truly (classical) chess player.
Both cases have nothing to do with with good manners and social behaviour. Some great masters where well educated but darn sarcastic on treating opponents.
Do you think there is a relation beetween them? Do you think personality is the reason why we have different playing styles? Come with your own examples