Most hays are cured grass though some places may have "meadow hay" that can be other plants. When cutting hay, they don't worry about having the seeds left on - seeds add nutrition and don't harm the animals that eat the hay. The seeds will sprout and once established, pasture grass is very hard to eradicate.
Straw is the stems of wheat, oat, or rye after the grain has been harvested. They really don't want to leave the grain heads on the straw - grain is too valuable and while straw is generally not intended to be eaten, animals do tend to nibble it. Some of the grains have husks or fibers that can be harmful to the animals, especially to horses.
I have problems with the deer - they come right up to the house to eat out of the bird feeders. I moved the feeders closer, next to a walkway, so they are four feet outside my window. The deer will come right up and are very bold and unafraid. I've opened the window to yell at them, and they just look at me like, "Hey, shut up - we're eating here!" They come up day or night, but eat more at night. So if I want to feed the birds without letting the deer eat 2-40 pounds of seed a night, I have to bring the feeders in every single night.
The raccoons are worse - they climb up the poles and knock the feeders to the ground to empty them. They'll even do it with hummingbird feeders. Then that attracts the opossums and foxes. Plus the raccoons fight with the cat and I worry about them learning how to get in through the cat door.
It's my own fault - the site where we built our new house was a grazing and hunting area for all the animals for over thirty years and we were careful to not disturb them. Then we plunk a house down in the middle of their territory and expect the animals to move on off. No matter than they have the rest of the 60 acres to roam in - they like this spot!