Why do some people refer to themselves as Persian and others as Iranian?

Question

Are they not the same country?

Answer 1

Although all Iranians, including Persians, have always referred to their land as Iran or other similar variations, the term Persia was adopted by all western languages through the Greeks and was used as an official name for Iran by the West until 1935. Due to that label, all Iranians were considered Persian. Therefore, many Western sources, when regarding Iran's history, will label many non-Persian Iranians as Persians, which distinguishes nationality, not necessarily the Persian ethnic group.

Also, many others who embraced the Persian language and culture are also often referred to as Persian, not necessarily meaning ethnic group, but rather as a part of Persian civilization (culturally and linguistically).

Answer 2

Persians are the direct descendants of the Medes. Their original religion is Zoroastrianism. Persians are actually Aryan and Farsi is an indo-european language. Arabs are a semitic people, and Arabic is a semitic language.
Because Persia was the crossroads of the ancient world, many ethnic groups settled there centuries ago. This collection of different groups are known as Iranians; the descendents of the Medes are Persian.
Besides, we call Americans of any ethnic group "Americans". Get the parallel?