MU’MIN OR MOMEEN
First and foremost, lets figure out the meaning of the word "Muslim". What does the word "Muslim", which we all use so often, really mean? A Muslim is one who surrenders his will to the Will of Allah. Now the question is, who are a Muslim and or a Mu’min? Can a person be a Muslim by virtue of his birth? Is a person a Muslim simply because he is the son or grandson of a Muslim? Is a Muslim born a Muslim family, just as a Christian`s son is born a Christian family, or Englishman`s son is born an Englishman? A Muslim does not become truly a Muslim simply because he is born a Muslim. A Muslim is not a Muslim because he belongs to any particular race; he is a Muslim because he follows Islam.
We all agree that we become Muslims only by accepting Islam. But what does acceptance of Islam mean? Does it mean that whoever makes a verbal profession -- "I am a Muslim" or "I have accepted Islam" -- becomes a true Muslim? Islam, therefore, consists, firstly, of knowledge, and secondly, of putting that knowledge into practice. Therefore Mu’min is a true Muslim who believes in what “Allah” سبحانه و تعالىhas revealed on the last and final messenger Muhammad ﷺand acts accordingly with knowledge and understanding of male and female companions of Prophet Muhammad 
There is a huge difference in the rewards and punishment in the eyes of Allah سبحانه و تعالى for a legal Muslim and a true Muslim (Mu’min) ... a person can still legally be a Muslim in this world, bearing a Muslim name and being born into a Muslim family, but in the eyes of “Allah” سبحانه و تعالى, a true Muslim (Mu’min) will only be the one who has knowledge of Islam and acts according to the Qur’an and Sunnah. These are the ones whom Allah has termed “Mu’mins” in the Quran and it is for these Mumins that Allah has promised a good reward in the hereafter.
Signs of believers as mentioned in Qur’an.Surah Muminum 23: 1-11
Further Allah سبحانه و تعالىsaid: “Whoever does righteousness, whether male or female, while he is a believer - those will enter Paradise, being given provision therein without account.” Quran.surah Ghafir or Momin 40:40
Whatever the situation, a believer does not change, Remember the words of the Messenger ﷺ: “How wonderful is the affair of the believer, for his affairs are all good, and this applies to no one but the believer. If something good happens to him, he is thankful for it and that is good for him. If something bad happens to him, he bears it with patience and that is good for him.” Sahih Muslim 2999. So if calamity befalls a Muslim, he must say “Inna Lillaahi wa inna ilayhi raaji’oon” (Verily to Allah we belong and unto Him is our return).
It was narrated that Abu Hurairah رضي الله عنه said: "The Messenger of Allah ﷺsaid: 'The strong believer is better and more beloved to “Allah” than the weak believer, although both are good. Strive for that which will benefit you, seek the help of Allah, and do not feel helpless. If anything befalls you, do not say, "if only I had done such and such" rather say "Qaddara Allahu wa ma sha'a fa'ala (Allah has decreed and whatever he wills, He does)." For (saying) 'If' opens (the door) to the deeds of Satan.'" Sunan Ibn Majah Vol1:79 
There are three levels of faith a Muslim person can attain. The first level is Islam. The second level is Eeman. Final is Ihsan,which is the highest of the three levels of faith and the closest to Allah سبحانه و تعالى. Below are the details given about individual levels of faith, Sahih Muslim Vol 1:1, 6.
1. The Creed (Shahadah),
2. Daily Prayers (Salah),
3. Almsgiving (Zakath),
4. Fasting during Ramadan (Sawm) and
5. The Pilgrimage to Makkah (Hajj) at least once in a lifetime, if you have means.
To belief in
2. The last day
5. Prophets Destiny
Ihsanis the highest of the three levels of faith and the closest to Allah سبحانه و تعالى. It is to worship “Allah” سبحانه و تعالىas That if you are seeing Him, for though you don't see Him, He,verily, sees you. Ihsan means that a Mu'hsin (a good Muslim) is sure that “Allah” سبحانه و تعالىis seeing him/her in everything he/she says or does. Therefore, a Muhsen does his/her best to say and do only what pleases “Allah” سبحانه و تعالىand conforms to His commands. This is the level of righteousness, the level of perfection, the level of doing and saying the ultimate good, the level of I'hsan.
Basically Ibn Taymiyya رحمت الله says that there are three levels 1) Muslim 2) Mu'min 3) Muhsin and last two of them are those who enter Jannah without being in Jahannam, i.e. without punishment. The first one will enter Jannah in any way, but he will be punished in Jahannam first and he mentioned Qur’an.Surah Fatir35:32 as an evidence for these three levels.
1) "thalim li nafsihi" (those who do unjust against themselves),
2) "muqtasid" (those who are balanced)
3) "sabiqun bil-khayrat" (those who are foremost in good deeds)
So based on this ayah scholars explained that there are three levels of Eeman:
1) "asl al-Iman" (The root of Eeman)
2) "wajib al-iman" (Obligatory Eeman)
3) "mustahab al-iman" (Perfection of Eeman),
Asl al-Iman; that's what is required for a person to become a muslim, because he has the root of iman. So basically a muslim will eventually enter Jannah. And all these ahadith of shafa'ah are about this group of muslims, those who have asl al-iman, they are regarded as muslims and will enter Jannah "Wajib al-Iman"; are those who besides asl al-iman has also combined "wajib al-iman". That means he performs all obligatory actions and abstain from all haram. That person is a real mu'min. He will enter Jannah without a punishment!
"Mustahab al-Iman"; they are those who besides first two levels of iman combine also the highest level of iman, i.e. they have higher level because of their extra a'mal. They have perfected their iman! And these group will also enter Jannah withour punishment and they will have higher level in Jannah. Majmoo’ al Fataawa 7/10
“Among the believers are men true to what they promised Allah سبحانه و تعالى. Among them is he who has fulfilled his vow [to the death], and among them is he who awaits [his chance]. And they did not alter [the terms of their commitment] by any alteration.” Qur’an.Surah Al-Ahzab 33:23 This means: If you change your trust level in “Allah” سبحانه و تعالى, your worship, or your straightness along with the change of your circumstances and status, then your actions negate the real belief in “Allah” سبحانه و تعالى, because a true believer in “Allah" سبحانه و تعالىis characterized by the Prophet's ﷺdescription: "If something good happens to him, he gives thanks for it and that is good for him; if something bad happens to him, he bears it with patience, and that is good for him. This does not apply to anyone but the believer."