Spacers = just a shim/washer type thing that moves the wheels away from the car... too much and you stress out the studs holding the wheel on...
Adaptors = remove the existing studs, use new short bolts to bolt the adaptor to the existing hub, new studs come from the adaptor, can be in a different pattern.
Say if you wanted to put cheby wheels on an ford. They have the effect of spacing the wheel out more.
Some adaptors are used just to do the spacing, if the studs may not be log enough... say you want to put a foxbody wheel on a classic mustang, the foxbody wheel goes too close to the chassis, so an adaptor/spacer might be used to push it back out, etc..... whaever...
Also known as a good way to die when the break, or the studs get over stressed and break.