What's the difference between the difficulty options?

Deus Ex: Human Revolution gives you three options for starting a new game, "Tell Me a Story", "Give Me a Challenge", and "Give Me Deus Ex":

The wording seems to imply that there's more difference than just tougher enemies (i.e. more/less emphasis on story), is there?

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)

This is taken directly from the strategy guide. Note that the player health always shows up as 100 ingame regardless of the difficulty but it is more of a percentage. You get more (50% more in this case compared to the next difficulty) out of your 100 health (or 200 max with nutrients), ie take more damage before you die, on Tell Me a Story than harder difficulties.

Tell me a story

• Player Health: 150%
• Player Health Regen: 115%
• Player Health Regen Delay: 75%
• Energy Regen: 150%
• Energy Regen Delay: 75%
• Enemy Accuracy: 60%
• Enemy Health: 75%

Give me a challenge

• Player Health: 100%
• Player Health Regen: 100% (4 pt/sec)
• Player Health Regen Delay: 100% (6.5s)
• Energy Regen: 100% (1 pt/sec)
• Energy Regen Delay: 100% (10s)
• Enemy Accuracy: 100% (per enemy)
• Enemy Health: 100% (per enemy)

Give me Deus Ex

• Player Health: 75%
• Player Health Regen: 85%
• Player Health Regen Delay: 115%
• Energy Regen: 75%
• Energy Regen Delay: 125%
• Enemy Accuracy: 125%
• Enemy Health: 125%

Starting a playthrough on Give me Deus Ex also disables object highlighting and the crosshairs, but these can be re-enabled in Options -> Gameplay.