On the left you have straw. On the right you have hay. Can you see it? Hay is greenish, dried grass. Straw is what’s left over once grain is harvested. One has plenty of nutrients, one doesn’t. There in lies the lesson. If you are FEEDING an animal, get hay. If you are mulching, making bedding, stuffing a scarecrow, get straw.
You can mulch with hay. It’s not very cost effective unless you have a connection with someone with loads of spoiled hay. But, since hay still has seeds in it, you will want to pile it DEEP so any weeds that find the ground, never find the sun. (See the The Ruth Stout No-Work Garden Book for instructions.)