Straw vs hay....
Stray is bedding. It has no nutritional qualities. It's the thick stems of oats, wheat, whatever, after the seed heads are harvested. Long, thick stems, no seeds or "good stuff" for anyone to eat. It's dry and brown, usually very stiff and prickly.
Hay is food. It's grass, what kind will vary depending on your region. Alfalfa, timothy, orchard grass, regular grass, oat hay (with the seed heats intact), pea hay.....whatever grass or legume is harvested, with the seed heads or other "good stuff" intact. The stems are finer and softer, it should be green if grass, golden yellow if legumes, and not too prickly to handle.
Large animals eat hay, and they eat the whole thing. My chickens, given hay, scratch through and eat the seed heads and other good stuff, usually leaving the stems. Even the fine stems aren't too appealing to the chickens. Those stems work great for the garden, as Mrs K said, or they make bedding, can line a nest box, compost, or be fed to a large animal--horse, goat, cow, etc.
So, just for something to walk on, straw is fine. For additional forage/food, hay is the way to go.