Two main types of worms are common in puppies. Roundworms are the more common and more serious parasite. Puppies usually catch roundworms from their mothers in the uterus or while nursing. Roundworms can spread to humans (especially children) and make us sick.
It isn’t common to see roundworms in a pet’s stool, even if the pet is infested. They are long, thin, and white when they are seen. Most of the time they look like vermicelli noodles.
The Companion Animal Parasite Council and other authorities recommend treating all puppies repeatedly for roundworms. Puppy dewormings usually are designed to remove roundworms.
Tapeworms are a second common type of worm. The most common type of tapeworm is spread by fleas (animals must eat a flea to contract it). Tapeworms are less dangerous than roundworms, although they also can spread to humans–if we eat fleas.
Tapeworm segments frequently are visible in the stool of infested animals. The segments look like rice grains (when wet) or like sesame seeds (when desiccated).
The most commonly used puppy dewormers remove only roundworms. They do not remove tapeworms. I’m guessing that you’re seeing tapeworm segments in your puppy’s stool.
There are, of course, other types of worms as well. I recommend that you take a stool sample to your vet. Analysis of the stool will allow identification and removal of the parasite.