What is the difference between energy efficiency and power efficiency of a CPU/GPU chip?

Either you want to talk about the performance per watt ratio, or the energy taking the memory into account as well. If you take the performance per watt ratio (PPW), then in the case of the GPU, it would depend on the application being run. Running a graphics application (requiring more parallelism) will provide you with a high PPW. However, running an inherently sequential app will use less cores on the GPU, so most of the energy will be wasted, lowering the PPW considerably. Also, a GPU core is much weaker than that of a CPU, and that'll also add to lowering the PPW. In the case of a say 4 core CPU, it should run sequential apps fairly well with a high PPW, while parallel apps wont scale much due to limited number of cores. If you take the memory into account, then GPUs mostly perform worse. This is because the GPU has a limited memory, and may have to get memory elements from the main memory (which means it would have to go through the GPU), which would result in energy wastage. The CPU will therefore perform much better in this case given the application uses a large memory footprint. The CPU and GPU are not meant to do each other's work, but with recent releases of multi-core CPUs (like the Xeon Phi), the gap seems to be closing down.

A simple way to look at it would be to know that Energy = Power x time. While a processor may be power efficient (consumes less power) to do a certain task; it also is important to know how much time it takes to complete that task in that state. Some designs throttle the workload so that the overall energy consumed is kept low even when the processor is at a high power state(by doing so for a very small amount of time).