Users can only create pages beneath a page for which they are in a role with "Create Child Pages Permission" and can only edit pages for which they are in a role with edit permissions. They are separate permissions. It seems reasonable that a user who has permission to create a page should also be able to edit it but they are separate permissions mainly to facilitate the use case where they can edit but not create child pages.
By default when creating a new page it will inherit permissions from the parent page so if you want the user to both be able to edit and create pages below a page then they should have both those permissions on the parent page.
Joe