A golem is crafted by an artificer, a magical engineer. They are effectively a robot or machine that's built for a specific purpose. They are usually precoded with a set of commands and then set loose. Sometimes they are summoned wholesale through magic, but usually NOT. Occasionally, they become sentient or even sapient, but that follows the same principle as sentient machines.
A Homunculus is created by an alchemist, a magical chemist. They are living, thinking beings that were created through magic. Artificial Human(or at least Being). Typically, they would be a familiar or assistant to the alchemist, but sometimes they are used as a new body for an ailing mage, or even as a servitor race by a God. Traditionally, they would be small, the size of a fairy, but that image faded away a while ago. Probably because of Full Metal Alchemist.