"Sentience," the noun form of "sentient," frequently heard in science fiction and fantasy, means the ability to perceive individual experiences. According to the Miriam-Webster Dictionary, the exact definition is:
sentient: 1: responsive to or conscious of sense impressions 2: AWARE 3: finely
sensitive in perception or feeling
"Sapience," noun of sapient, is the ability to think, and to reason.
sapience: WISDOM, SAGACITY
It may not seem like much a difference, but the ability to reason is tied more closely to sapience than to sentience. Most animals are sentient, (yes, you can correctly say your dog is sentient!) but only humans are sapient.
For further reading on the difference, check out these articles:
Wikipedia SapienceWikipedia SentienceAskDefine Sentience (of particular interest is the user-contributed dictionary)
("The Word Box: Sapience vs. Sentience", Rebekkah Niles)