Hay and grass have many similarities, but they are not the same. Hay refers to grass that has been cut and dried. It is often stocked for different purposes such as to be used as animal fodder. It is mostly used as fodder for animals such as cattle, goats, sheep, and horses.
The grass is any plant that belongs to the family of Poaceae. It is characterized by leaves that arise from the nodes of the stem. The leaf bases also wrap around the steam. It is a large family that consists of monocotyledonous flowering plants.
You have to realize that hay is grass but the hay is the dried version of grass. Hay is usually stocked because they are used for different things. There are some that are used to feed the animals while there are also some that are stored for future use.
Hay is normally used to feed herbivores but there are instances when pigs can be fed with hay too. They may just have a harder time digesting the hay because their systems are not meant for that. There are also some animals that can be fed with grass better because of the water content of grass that hay does not have anymore.