There are many different types of hay, each with its own benefits.
Alfalfa:
A palatable hay that horses like the taste of, this hay if often used to make cubes and pellets. It is easy for animals o digest and high in protein, energy, vitamins and minerals. It is also produced and sold in every state of the US.
Bermuda
Has been thought to cause impaction in horses when low quality, so buyers should be VERY aware of the hay they are purchasing. Animals generally like the taste of it.
Clover
When dried, clover hay doesn't preserve the green colour and becomes dry looking. Clover is often mixed with grass hay and comes in red, white, crimson, alsike and landino. Also if this hay becomes damp and you feed it to an animal, the mold can make the animal very sick.
Orchardgrass
This hay isn't as nutrient rich as the alfalfa hay, it has good flavour and is high in fiber.
Tall Fescue
This hay can be damaging to pregnant animals, however it is soft hay and long which also turns yellow as it dries.
Timothy
This hay is way easier on the digestive system, instead of some others. It is high in fiber and low in calcium content. This hay can be more expensive than others, but it is high in nutrients for aged animals.
That is all I know about some types of hay (my uncle had a farm) As this information might not help, I can upload some pictures of the hay and you can see which one is yours x