What is the difference between genitive case and possessive case or are they same?

They are very nearly the same, but the genitive case in many languages has functions that go beyond mere possession. For example, in Latin the genitive case encodes not only possession (domus patris mei, "my father's house") but also other relations between nouns, such as the material out of which something is made (flumina sanguinis, "rivers of blood") and the object of an implied verb (cupiditas argenti, "desire for money"). Note that in English, which has a possessive case ("John's", "his", etc.), we can say "my father's house", but not "blood's rivers"; and while we can perhaps say "money's desire", it means something quite different from the Latin version.