What is the difference between the difficulty levels?

Minecraft is at the very limits of my computer's capabilities. I have to set the render distance to tiny. And even then, when a creeper gets close the screen gets choppy and I die almost everytime. I lowered the difficulty to peaceful but I can't tell if there are any bad guys at all. Without that tension the enjoyment has lowered.

So what is the difference between the difficulty settings and what other settings can I choose to help my computer run the game more smoothly?