Hay is cut during the early stages of growth. The younger the plant is when the hay is cut, typically the higher protein and nutrition in the hay, when compared to the same plant. The best hays are usually cut before the plant flowers. Straw, on the other hand, is allowed to set seed and mature before cutting. This increases the amount of fiber and decreases the amount of animal available nutrients in the plant.
Straw is typically a by-product of the grain industry.
Good hay should be green and smell fresh. Hay will last for as long as a year without losing any significant amount of nutrition as long as it is kept dry and out of the sun. Wet hay will mold and the moisture can cause nutrients to leech out of the hay. Direct sunlight will cause nutrients to break down. Stray has higher fiber than either, and lower protein levels.