A wheel spacer is generally a smaller, universal single piece of steel/aluminum, designed to work on a variety of cars and to give minimum spacing, usually less than 1/2". They fit directly onto the studs, and are sandwiched by the wheel and the hub. Wheel adapters are usually heavier, and thicker pieces that are machined, are designed for specific applications, and generally have their own studs. The adapters bolt to the stock studs, then the wheel is bolted to the studs on the adapter. Adapters are usually used to provide spacing greater than 1/2" (I've seen adapters that are 2+ inches thick), and they can also be used to alter a bolt pattern, like if you ever want to put Vette rims on a mustang to try to make it look sorta cool :)
Spacer:
Adapter:
Spacers are generally only used to give a slight stance improvement, but if they get too thick then they will lower the amount of available threads on the studs, and may pose a safety risk. Adapters are much better for larger spacing, but physics tells you that you should only push the wheels out so far before they become hazardous due to downward force and the weight bearing on the suspension, that's why you sometime see the ricers with the wide wide wheels tracts and the back wheels look like this /-==-\
[Modified by 86Coupe, 11:21 AM 4/4/2002]