Lesson time for everyone! Hay is grass that has been cut and dried. Grass that has not been cut and dried is fresh grass. It can't be called hay if it's not dried. You can grow your own various types of grasses such as Timothy, Orchard, Bluegrass, Bermuda, etc., but it's not hay unless you cut it and let it dry on the ground for a couple of days and then you can bale it or you can put it in a airy cardboard box or something for storage in a cool place. I used to work in hay fields putting up bales of hay.
Feeding fresh grass is good for the pigs but they still need the hay as it helps to wear down their teeth and helps aid in digestion.