In the Quran, I found the terms used in three ways:
1. a mumin is asked to be mumin.
4:136 O ye who believe! Believe in Allah and His messenger and the Scripture which He hath revealed unto His messenger, and the Scripture which He revealed aforetime. Whoso disbelieveth in Allah and His angels and His scriptures and His messengers and the Last Day, he verily hath wandered far astray.
2. a mumin is aksed to be muslim.
2:208 O ye who believe! Come, all of you, into submission (unto Him); and follow not the footsteps of the devil. Lo! he is an open enemy for you.
3:102 O ye who believe! Observe your duty to Allah with right observance, and die not save as those who have surrendered (unto Him).
3. a muslim is asked to be mumin.
49:14 The wandering Arabs say: We believe. Say (unto them, O Muhammad): Ye believe not, but rather say "We submit," for the faith hath not yet entered into your hearts. Yet, if ye obey Allah and His messenger, He will not withhold from you aught of (the reward of) your deeds. Lo! Allah is Forgiving, Merciful.
The terms ?Iman? and ?Islam? have been used in various way to denote different states of a person?s affairs and from different perspectives.
I wish to add with what has been said in the article. As I understand, Iman and Islam are related to each other like seed and plant, where both the seed and the plant grows, and both interacts with each other and one affects the other. Basically, Iman is the life-world-view, the mentality, the attitude and the tendency of a person, and Islam is the pattern of behavior of the person that springs from Iman. This is from the perspective of first-person-position or the introspective method by the person, or the position of God.
Iman and Islam has got other connotations which is related to the legal aspects of the community of the believers where things are judged from behaviorist point where data are processed from human-third-person-position. From this perspective, a hypocrite is also considered a mumin and a muslim if he conforms with the minimum acknowledgement of commitments to the community and the minimum levels of activities as expected by the community.
The Quran?s usage of the terms encompasses all these areas.