As I understand it, Apple publishes ibooks. E-books, on the other hand, which are simply digital books - with or without interactivity - are published by all sorts of publishers, traditional and otherwise. Some companies that specialise in e-books for children are: Meegenius, Nosy Crow, ITB, Ruckus Media, Utales... I will probably remember more at some point and will update with more info.
ibooks, however, is simply the Apple version of the Nook store, or the Kindle store. It's the Apple branding for their digital books.
PS You can get your book published with ibooks/Apple relatively easily. Well, I say that, you have to fill out some forms and apply and wait for approval. But it's doable!