How is it that my camera plays 1080p video perfectly smoothly (in camera outputting to HDMI to tv) but...,?

my pc stutters and lags and makes the footage really jerky. The pc processor is 2GHZ, which is surely many hundreds of times faster than the camera's microprocessor, which is probably an ARM or a motorola chip. Plus, the pc has 4gb of memory, whereas the camera probably only 64mb or 128mb. Could someone technically knowleadgable explain this to me?