Parsis were the first migrants to India, they came over 1000 years ago although I think there were other migrations. Parsis have some Indian admixture, about 25% on the maternal side.
Iranis were more recent migrants from Iran, escaping Qajar persecution. They came towards the end of the 19th century and early 20th century. Most of them have mixed with Parsis by now and have been absorbed by the greater Parsi community. The distinction is only seen in last names, but everyone identifies as Parsi.