In puppies it means removal of the dew claw, which is a 5th claw, located higher up the leg. It is done when they are a day old and is considered painless. It's very common as the dew claws catch on things, are not necessary to the dog and not well attached to the leg.
Declawing in cats does mean what you think it means, involves amputation of the tip of the toe at the knuckle and is not painless