Carbon Taxes vs. Cap-and-Trade

Ezra Klein, Matt Yglesias, and Kevin Drum pile on Thomas Friedman for implying that carbon taxes and cap-and-trade systems are different. (Actually, Friedman asserts that none of the major candidates have proposed a carbon tax.)

I understand how a carbon tax works: If you sell a carbon-burning commodity, the tax is collected. But I keep falling and can't get up when I think about cap-and-trade: Who needs to buy an emissions permit? A refiner? A power plant? A farmer? An automobile manufacturer? A car owner? A farting cow? And, once you've defined who needs one, how do you enforce it?

It sure seems like the two really are different. One taxes fuel production, while the other taxes emissions.

I've always kinda liked the free market spirit embodied in cap-and-trade. But there are a lot of details to nail down. Why isn't a carbon tax simpler and easier to enforce? Is it merely because it forces legislators to go on record and state what they think the cost of emissions really is? Doesn't somebody have to do that when they set the supply of cap-and-trade permits?