Poll : What is the difference between Persian and Iranian?

Persian is also an ethnicity

not just a former nation.

There is still a Persian language (Farsi), for example, and though that is the (only) official language of Iran only about 53% of Iranians speak it natively. It is also an official language in Afghanistan and Tajikistan.

Persia was conquered by the Muslims early in the history of Islam

and though the Muslim government made a powerful effort at Islamicization from the beginning (through active government-funded missionary efforts and legal oppression of Zoroastrianism)

it took quite awhile (centuries) for Zoroastrianism to be (essentially) eradicated in Iran. Only an extremely small percentage of the population of Iran is Zoroastrian.

It may be that someone you know is equating Persian ethnicity with Zoroastrianism

and, indeed, many ethnic Persians are Zoroastrians

but I'm pretty sure that the great majority of ethnic Persians today are Muslims, not Zoroastrians.

Both are the same.  Persia comes from the Ancient Greek name for the place. Iran is the name favoured by locals.  The English speaking world switched from saying Persia to Iran at the request of the Shah in 1935.  Zoroastrianism was the main religion of Iran before 651 when it was conquered by the Rashidun Caliphate who imposed Islam.  Many Zoroastrians fled to Northern India where they remain and are generally called Parsi (Persians).  Interestingly, Jews are tolerated in Iran.