Hay is for animals to eat; straw is the leftovers from harvesting wheat or marsh grass or oats or barley; its bedding for the animals.

Well, spoiled hay which you would not feed to your Cattle Herd!
(Everyone uses sour milk in their coffee right?)
Available at a local garden center, EZ Straw with most of the seed removed!
I several bales of Rice Hulls that I have been using as mulch. High Silica content so good for soil amendment.
My Red Kuri and Bush butternut squash which are starting to "race" around around the garden and I will be getting some EZ straw before they start to really explore. (Killed my first squash nymph yesterday...Got a lure trap that has snagged a number of Transparent Wing moths before they could lay their eggs! Fun!)