Shoe mouldings are used along the bottom of a base moulding along a finished floor and are generally used for one of two purposes. The first of which is to cover up any additional gap created between the flooring and baseboard (often if flooring is installed after baseboard is already in place) and, secondly, to create an extra built up detail in a base moulding.
Stop moulding is used typically on a door unit to prevent the door from swinging into a room. You will commonly see it along the edge of a door that is set into a door jamb. While this is by far it's most common use, a door stop can also be used as a decorative accent, or even as a shoe moulding, creating a unique additional profile to your baseboard as opposed to the often used quarter round.