All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Muslim can be called either Muslim or Mu’min. Iman, in this case, is synonymous to Islam. But when Iman is mentioned on its own, it is different from Islam. Each one has its pillars. The five pillars of Islam are saying the Shahadatayn (The Two Testimonies of Faith), performing the five obligatory prayers, giving the Zakat, fasting in Ramadan, and performing the pilgrimage (Hajj) for those who can afford to do it. The six pillars of Iman are: believing in Allah, believing in His Angels, His Books, His Prophets and believing in The Last Day and in Destiny be it good or bad.
In fact, Iman is more highly ranked than Islam as it is more specific. This means that every Mu’min is a Muslim, but the opposite is not true.
For more benefit, please refer to Fatwa 84243.
Allah knows best.