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No. "Tell me a story" does not mean that the story is enhanced. Rather, it means that the challenge is decreased, as if to say that the game is only interesting for its story and not its gameplay challenge if the player picks the reduced difficulty.

To be specific, harder difficulty decreases your health and regeneration rate, increases the enemy's health, regeneration rate and accuracy. It also affects the regeneration delay. (Source: GameFAQs)

I knew there was a shop in the first city hub that sold them, but a quick check on the wikia page gives a fuller breakdown:

• Purchasable at from Seurat in the Detroit Apartments 2nd floor (accessible through fire escape by the basketball court).
• Purchasable in Hung Hua Hotel 1st floor.
• Found in a drawer in Montreal - Online News Division (Level 3).
• Quest reward from Smash the State (Act 4) Detroit by Knocking out target "White" instead of killing him.

This doesn't seem like many, but they can only be used on the 10mm Pistol, Combat Rifle and Machine Pistol anyway.