TDP ~ average power draw (though average power draw at full load for Intel's and Nvidia's specced devices tend to be a bit below rated TDP rating, vice versa for AMD's TDP rating). Almost every watt of electricity you put into an IC will be turned into heat, with the output 'power' from bus interfaces being a mere rounding error.
Peak power draw can have transients well above average power draw (indeed, over longer durations this gap between TDP and peak output is what allows 'turbo boost' to exist). For normal ATX/SFX/FlexATRX/1u supplies that actually meet the ATX specifications this peak load is a nonissue, as the ATX spec requires them to handle high transient load spikes like this. Even for DC-ATX supplies, transient loads should not be a problem.
The problem comes when you use non-ATX supplies, namely laptop bricks. Laptop bricks are designed to charge a laptop battery, which has a nice stable steady power draw. They are not designed to handle spikes in load and do not have the components to safely deal with them, so instead have 'agressive' overcurrent protection that will cut out the power supply if you go even a bit above the rated spec (or they have no overcurrent protection and the power supply just fails and lets out the magic blue smoke).
It is in this case where you need to aim top use a brick whose rated power output is at or above the peak power load your components can draw. Even that is not always enough, because the rate of change of power draw (the 'slew') can also trip protection if it is too fast (again, ATX compliant supplies have to hit a minimum slew rate of 2.5 amps per microsecond. Laptop supplies do not). The R9 Nano, for example, ramped up and down its power draw so aggressively that it caused laptop bricks to trip out even when their raw watt rating implied they could handle the peak load.
