the disc drive is the same in both models
what makes the slim smaller is the reduction of size in the processor.
a more efficient procesor runs cooler, negating the need for a massive shell. sony also removed the larger power source in the fat models with one more akin to the old fat PS2.
so smaller/ more efficient processor means smaller motherboard, less heat, and asmaller demand for energy. that is why the slim is smaller. not the size of the drive itself.