Preschool, nursery school, daycare, prekindergarten....there are a lot of names! To me (a preschool teacher) preschool is the broadest -- it mainly refers to the time between three and five, before a child goes off to elementary school.
Nursery school is what they USED to call it, when I was little. It referred to a regular program for 3 or 4 year olds where they went either half days or a few mornings a week to play, have snack, make friends, etc. Now those are generally called preschools.
Daycare centers have preschools, too -- the classrooms for the 3 and 4 year olds are preschools, and they use preschool-appropriate curriculum and materials. My children went to a Montessori daycare center and their preschool experience was absolutely incredible.
Then there's prekindergarten, or pre-K, which simply refers to the year before the child goes to kindergarten. I teach a program for children in their last year before kindergarten, so mine is a pre-K program.
Nobody HAS to go to preshool. The children who really, really should go to a high-quality program are the children living in poverty who aren't going to get what they need (to be ready for K) from their parents. Children with SAHMs who read to them, take them places, talk to them, provide them with social opportunities, and thus can get along with others, have basic academic skills, can solve problems, pay attention, and speak clearly are fine just going off to K.
It really depends on what your child is like as he gets older, and also what you want. He may be very social and just have a blast going to preschool three mornings a week, and you may be delighted to have that time to yourself.