What is the difference between Muslim, Mumin, and Muhsin?
If you are an Arabic reader you can check a detailed explanation for the Hadith That was a conversation between the Prophet PBUH and a foreign Arab who came to ask about Islam, Iman, and Ihsan.
The difference between these three is the following:
Islam is to certify that there is one God, pray 5 prayers per day, fast Ramadan, pay zakat, and go to Hajj for those who can.
Iman is to certify the presence of God, his Angels, his Books, his Messengers, Doomsday, and Predestination (Good and bad ones).
Ihsan is to Worship God as if you can see him, if you didn't see him, know that he does.
So as a summary the difference is that Islam is to be done with your actions, however Iman is more related to your heart and beliefs.
In the verse 49:14 we can see the difference between Islam and Iman.
Ihsan is the most highest level among them. This verse 16:128 shows how the Mohsin has a high grade from his God, because of the fidelity between a person and his God.