Construct is the name given to a non-living thing that has been given life. They can be natural or artificial.
Golems are made of stone, clay or other earth-like materials. They often defend mountains, caves or nature shrines. They can also be built, and will protect whoever or whatever created it.
Elementals are primal beings, made of Magic. Specifically, they're made of a highly specified element, such as fire or water, however they can also be made of other things such as fear.