'Islam' means submission to the will of God, and a Muslim is one who submits to God. Allah is the Supreme Being, the one and only God. Like the Vaisnavas, Muslims practice bhakti-yoga because God is the target in the Muslim religion. The Muslims accept the personal conception of God, as the Christians and Vaisnavas do, and they acknowledge "Allah akbar", "God is great." Allah is the personal name of God as used in the Holy Qur'an. The Lord has many names, and chanting the holy name of Allah is non-different from chanting the holy name of Krsna.
Sometimes the Personality of Godhead descends Himself. At other times, He sends His confidential servants to alleviate the suffering of the living entities. Muhammad introduced himself as the servant of Godhead, Allah, and he preached the transcendental message of the kingdom of God. Muhammad is therefore an acarya for the Islamic faith. Vaisnavas accept Muhammad as the representative of God and whatever he says, we accept.
One of the scriptural injunctions in Islam says, "The more you strive towards Me, the more you love Me, the closer I come to you." The ultimate goal of Vaisnavism is learning how to love God, and the Bhagavata says that a religion which trains the followers how to love God and serve Him is a first-class religion. Consequently, Islam, like Christianity, is a basic form of Vaisnava dharma because all three encourage a relationship of loving service. While Vedic literature provides extremely detailed information on how to love and serve God, and on who God actually is (his name, form, personality, pastimes, etc.), the Qur'an (like the Bible) provides almost no information about who God actually is. This is one of the differences between Islam and Vaisnavism. All religions accept God, but they cannot give an explicit idea of God. One may say "God is great", but who is that God and how is he great? One should know who God is and how He is great - that is perfection.
Muslims do not believe in the Vedic literature, and anyone who does not believe in the Qur'an is called "kafir", or a rejector of the truth. Similarly, the Christians say that anyone who does not believe in the Bible is a heathen, and the Vedic literature refers to one who does not believe in the Vedas as "nastika". At the same time, Vedanta teaches that we must follow the great personalities, the great acaryas. That is the process for gaining knowledge. One must approach a spiritual master and learn from him. Whatever the spiritual master says is accepted: sadhu guru sastra vakya. Real evidence must be stated in the scriptures, and it must be explained by the spiritual master or saintly persons. Then it is considered evidence, regardless of the religious context within which it is presented in a given time, place, or circumstance.
Another significant difference between Islam and Vaisnavism is that Muslims are against Deity worship. Today's followers of Islam have no knowledge about the real form of the Lord, and therefore they say He is formless. Islamic art never depicts the face or form of the Lord. Instead, God is seen in the form and pastimes of the saints, or in the temple architecture or paraphernalia. Muslims reject worshipping the Lord's personal form because they fear the tendency for degradation of the pure form by material conceptions. Alternatively, the Vedic injunction is that one must strictly guard against conceiving of the Lord's spiritual form to be in any way material.
Like all religions, the Islamic faith has experienced reinterpretation and change of the original precepts over time. While the prophet Muhammad established five times for daily prayer, many Muslims today have adopted a change to three times for prayer. On the matter of deity worship, the Sufis, who are said to be the original cult springing from Muhammad, accept the personal aspect of the Lord and speak of the Lord's form in their poetry. But generally, that level of personal conception is no longer accepted today.
Bhaktivedanta Book Trust. Excerpted from various texts and purports of HDG A.C. Bhaktivedanta Swami Srila Prabhupada.