Are all Ishmaelites Muslims?

Muhammad, the prophet of Islam, was a direct descendant of Ishmael through his second son, Kedar. Muhammad received revelations from an angel whom he believed to be Gabriel. These revelations later became the book of the Muslims, known as the Qur'an. Muslims believe that Abraham took his firstborn, Ishmael, to the altar of sacrifice on the mount instead of Isaac to substantiate Ishmael as the seed through which the whole earth would be blessed. The Muslims also believe that Muhammad was the fulfillment of God's promise to Abraham and that Muhammad was the prophet like unto Moses. They consider the Christian Bible to be changed and not entirely authentic. The nation of Islam comes forth from Ishmael's descendant, Muhammad. So Islam's roots trace back to Ishmael, Abraham's first son.

Later Ishmael married an Egyptian and his family vastly expanded through 12 sons, leading to a multitude of people. The Muslim people existed long before they embraced Islam.

—Faisal Malick, The Destiny of Islam in the Endtimes, pages 22, 23