Pre-School or Pre-K?

Maddie is starting Pre-School in the fall. Or maybe it is Pre-K?
I get confused between the two. Regardless - she is going to all day school for 3 year olds. The amount of stuff that they need to sign her up is kind of nuts. First -we had to fill out the application. Then we had to write a check to cover the registration fee. Then we had to write another check to cover the registration for after-care. Then we needed to fill out the bank information so they can deduct the tution straight from our checking account. Oh - and they needed a voided check. Then we had to go to the doctor - which we do every year - but the doctor had to fill out the medical forms and we had to get a print out of all the vaccinations that she has received to date. Then - the last thing they need is her birth certificate and her baptismal certificate. So - I went on a mad hunt tonight trying to find both of these items. Luckily I had copies of her birth certificate with her keepsakes. (The real copy must be in the safety deposit box). However - I don't think I ever received a baptismal certificate. I don't have it anywhere. I think I need to call our church and get a copy from them. I really have no idea. This is all new to me. I know I will need it eventually for her 1st Communion and Confirmation and all that good stuff to come.
It is just nuts all the stuff we have to do for a 3 year old.