Undoubtedly, there is a great difference between a believer and Muslim or Iman and Islam, in other words. Iman is both verbal and actions. Meaning, the heart and tongue confess with Iman while the heart and other sense do actions. Islam, on the other hand, means to submit oneself to Allah and obey His commands. Allah Almighty says,

The Bedouins say, "We have believed." Say, "You have not [yet] believed; but say [instead], 'We have submitted,' for faith has not yet entered your hearts. [Al-Hujurat: 14].

Based on this, scholars consider Iman as the inward deeds, while Islam is the outward actions. This is because Iman principally is the belief instilled in one's heart and Islam is to submit one's senses to it.  

Therefore, the true Muslim is not reluctant in submitting himself in humiliation to Allah obeying His commands, hastening to fulfill the obligations of Islam, abandoning its prohibitions and believing that what Allah commanded us to do is in our best interest and what He prohibited entails evil.   

�         Here, it is worthy to mention that both Iman and Islam are frequently interchangeable. The Arch angel Jibril (peace be upon him) differentiated between Iman and Islam in the well-known hadith [tradition] where he asked the Prophet (peace and blessings be upon him): "Oh Messenger of Allah! What is Iman? He replied: it is to believe in Allah, His Angels, Books, Messengers, the last Day, and destiny whether good or evil. And what is Islam? The Prophet replied: It is to testify that there is no god but Allah and that Muhammad is His Messenger, perform prayers, pay zakat [obligatory charity], fast the month of Ramadan and go for Hajj upon having the means." 

In the above hadith, Iman is mainly associated with inward actions or the deeds of the heart, while Islam is associated with outward actions or deeds of the senses. Even when the testimony of faith is counted among the verbal actions of Iman; it is, however, reflected in the explicit acts of worship of Muslims including prayers, fasting, zakat and Hajj. 

On the other hand, the Prophet (pace and blessings be upon him) defined Iman as Islam in the hadith narrated by ibn 'Abass on receiving the delegates of the tribe of 'Abdul-Qays. The Prophet (peace and blessings be upon him) said: "I order you (to do) four (things): to believe in Allah, that is, to testify that there is no god but Allah and that Muhammad is His Messenger, offer prayers, pay Zakat and to pay the Khumus (i.e. one-fifth) of the war booty to Allah." Here, the prophet (peace and blessings upon him) explained Iman likewise Islam.

To conclude:

Islam is interpreted in its absolute sense through the explicit acts of worship: saying the two testifications of faith, offering prayers, paying zakat, fasting and performing Hajj and so forth. These acts are considered the five pillars of Islam.

Iman includes verbal deeds, actions and strong belief: the heart and tongue admit with faith while the heart and senses work for it. Verbal deeds include remembering Allah [Dhikr], reading Qur'an, supplicating Allah, enjoining what is good and urging others to do it, forbidding what is evil and warning others against it, teaching and guiding those who go astray to the right path, sending or answering back greetings and the like.

On the other hand, one's actions spring form his heart and are reflected upon his senses. Meaning, the heart loves or hates for the sake of Allah, satisfaction with Allah's destiny, patience in times of afflictions, fearing and seeking His pleasure, putting our trust in Him and asking Him for forgiveness. The actions of senses include: bowing, prostration, standing and sitting before Allah in prayers, Tawaf [circumambulating the ka'ba] in Hajj, Jihad [fighting in the cause of Allah] and so on and so forth.