I would like to know the status of non-Muslims who are living in an Islamic state... the difference between an Islamic state and a Muslim state.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

An Islamic country refers to a land where the teachings of Islam are in effect and where all non-Muslims feel-safe with the covenant given to them by Muslims. Such a country is governed by Muslims and the Shari'a is in force, i.e. Shari'a regulates all affairs of such a society: worship, economy, policy, education, personal life, etc.
It is not a condition that all inhabitants of the Islamic country should be Muslims, since the rule in this concern is putting Shari'a into practice. If most Shari'a rulings and regulations are not put into effect and non-Islamic rulings take their place, then such a country is not an Islamic country even if its inhabitants are Muslims.
Allah Knows best.