"Sufism" is the correct term for the mystical tradition of Islam.
Islam tradition is reading quran and pray and do what prophet mohammed (PBUH) did
Sufism is mainly practiced by the Muslims. But the Hindus, the Buddhists and the Christians also practice Sufism.
Kabbalistic writings are contained in the Zohar.
Neither Orthodox Sunnis nor Orthodox Shiites are terribly mystical. The mystical form of Islam is best known as Sufism. Most Sufis are considered Sunni Muslims, but live and act in a way quite different than the Orthodox Sunnis.
The major tradition of Islam is following the five Islam pillars and belief in God, all God prophets, angels, all God holy books, the second eternal life, and God destiny. Refer to questions below for more details.