Laptop and notebook are the same thing. They can have large screens, dvd burners and powerful workings making them suitable for desktop replacements and are good if you don't intend carrying it about much as they can be quite heavy.
A netbook has a smaller screen, usually (but not always) a smaller keyboard and no cd or dvd reader. They are not very powerful but are fine for accessing the internet on the move, as they are lightweight. They have a smaller hard drive (usually) and are no good for video editing or other demanding tasks.
It very much depends on how your daughter will use it as to which will be most suitable.