dumb question... ftm-birthing center

It's past midnight and I've been up for about 20 hours straight so forgive me in advance. Ummm... is your hospital bag your diaper bag? Do you take bottles, diapers, wash cloths, swaddling blankets, sets of clothes, wipes, etc?? I will be giving birth in a birthing center and not a hospital so I'm really starting to wonder if I'll have to take my own things for the baby?