These are the most common roundworm found in dogs they are picked up from the mother both across the placenta and in her milk so virtually all puppies will be infested. 

And these are the most common worm found in cats this time it is a tapeworm you may well see these rice grain sized segments stuck to the fur near the anus. They have the flea as an intermediate host so when you treat your cat you must treat for fleas as well.