They are basically the same thing but can be characterized by Size and weight,
A laptop is bigger and heavier than a notebook.
A notebook as its name suggests is around the size of a A4 notebook and is lighter/thinner than a laptop.
A netbook is smaller than a notebook (usually around A5 size) and as consequence typically will have scaled down features.
As to what to get the wife all depends on what she wants to do with it. You would not want to do any serious work on a netbook for a period of time as the size and processing power make it a pain.
If portability and functionality are your key objectives then a notebook is the way to go.
If its going to be pulled out and used on a table now and then a laptop is probably best as they cost the least and although chunky can be moved around easily but you would not want to be carrying one around with you all the time.
If your not planning on any games being played on your purchase then dont worry too much about the graphics - but integrated onboard graphics is a big no no if you do want any sort of graphics performance with games.