Though their names sound similar, probiotics and prebiotics are separate entities, and the difference is in the name: prebiotics prepare an animal’s body for proper usage of the bacteria in its digestive tract as well as fuel the beneficial bacteria in the large intestines. Probiotics, however, create a culture where the “good” bacteria can grow and encourage healthy intestines.

Both promote better digestion and an increase in beneficial bacteria, but there are a few key differences between the two and their appropriate usage.

Probiotics

Probiotics stimulate the growth of beneficial bacteria in the intestines of dogs and cats, and they do so because the probiotics are deposits of bacteria that will be ingested by an animal, then put to work in the intestines. Because probiotics are living microorganisms, they must be processed and stored in an environment conducive to their survival, meaning that it may be difficult for them to be effectively added as an ingredient in normal pet food. Instead, probiotics may be given orally through a pill, syringe, or added to the food.

Prebiotics

Prebiotics are tiny nondigestible fibers that help fuel the beneficial bacteria in the large intestines of dogs and cats. They help keep pets’ digestive systems functioning at full force, and because they are fibers, they are easily embedded in everyday cat or dog food.
There are two common types of prebiotics:

• Fructooligosaccharides
• Source of energy for good bacteria
• Inefficiently used by bad bacteria
• Encourages growth and efficient use of bacteria by intestines
• Mannan oligosaccharides
• Contains sugar mannose, which discourages attachment of bad bacteria to wall of intestines
• Encourages bad bacteria to pass through digestive tract without causing a reaction
• Allows beneficial bacteria to grow without threat of harmful bacteria

http://www.petplace.com/article/cats/keeping-your-cat-healthy/feeding-nutrition/probiotics-prebiotics-for-cats-5-reasons-vets-recommend-them