You can already guess based on their names what these two are used for. The handloom is the type of loom that you will use when you want to weave cloth or do patterns. This time, you are going to loom without any machine that makes use of electricity or any sort of power. You would use your hand to weave. The power loom is considered to be the modification of the handloom.
In fact, this may be the reason why there are not enough handlooms that are available anymore. There are now different machines that will be more efficient in doing the needed looms in a short amount of time. This can be 10x faster as compared to the handloom.