What is the difference between Persian Gulf and Arabian Sea?

The Persian Gulf is known to be smaller as compared to the Arabian Sea. They are obviously two different bodies of water. You can find the Persian Gulf in between the Arabian Peninsula and a country, Iran. You can find the Arabian Sea in between the Arabian and the Indian Peninsula.
There are instances when the Persian Gulf is referred to by people as the Arabian Gulf, but it would depend on what people are saying. One of the reasons why the Persian Gulf is considered to be very special is the amount of crude oil that can found in its coastal areas. This is obviously one of the main sources of oil in the world as oil is exported to various places.