A Tarīqah is a school of Sufism, under the guidance of a Murshid (leader or spiritual director). The Murshid can trace his spiritual lineage back to the Tarīqah's founder, and on to the Prophet Muhammad.
Most Turuq (plural) are named after their founder, and when the order is referred to as a noun -yah is usually added to a part of the founder's name.
Turuq have historically played a major role in the expansion of Islam - particularly obviously in sub-Saharan Africa, central Asia, and south-east Asia.
Sufi groups which go beyond Islam
A number of "non-traditional" Sufi schools/organizations have developed in recent decades, mainly (but not exclusively) in the West. They tend to see Sufism as a universal spiritual quest/philosophy predating Islam, independent of the Qur'an and the teachings of Prophet Muhammad. Some of these groups are much more open to other spiritual traditions.