The term used for transfer of pollen grains from anthers of one plant to stigma of a different plant which, during pollination, brings genetically different types of pollen grains to stigma, is :

The correct answer is Xenogamy.

To understand why this is the correct term, let us break down the different types of pollination mentioned in the options:
1. Xenogamy: This refers to the transfer of pollen grains from the anther of one plant to the stigma of a genetically different plant of the same species. Since the pollen comes from a different plant, this is the only type of pollination that brings genetically different types of pollen grains to the stigma.
2. Geitonogamy: This is the transfer of pollen grains from the anther to the stigma of another flower on the same plant. Although it requires a pollinator (functionally cross-pollination), it is genetically similar to autogamy (self-pollination) because the pollen grains come from the same plant.
3. Chasmogamy: This refers to pollination occurring in open flowers with exposed anthers and stigma.
4. Cleistogamy: This refers to self-pollination occurring in closed flowers that do not open at all, ensuring autogamy.

Therefore, the term for pollination that brings genetically different types of pollen grains to the stigma of a different plant is Xenogamy.