The terrorism is an act of violence which basis is a political issue, and it is causing a political response.
The genocide is a systematic killing of people based on their ethnicity, race, or religion.
Example for terrorism is the attack on the twin towers in New York, when both of them were knocked down because of political reasons by Muslim extremists.
Example of genocide is the mass killing of Armenians by the Turks because of their religion and ethnic background.
There can be occasionally confusion about what is terrorism and what genocide, as lot of time both of them can take place in the same time by the same people. Also, some people neglect the definitions on what is what, so often consider a purely terrorist attack as a genocide, especially if a certain group of people was targeted, or a genocide would be considered as a terrorist attack despite being no political reason for the act.