The Sufis to me seem more syncretic — like the Bekhtashis (or are they the same?) — combining aspects of Bhakti Hinduism with Islam.
I think the Sufi came first. I’m not knowledgeable about the Turkish mystics beyond their religious “dancing”. My interest in India lead to what I know about the Sufi and the blending of Islam with Hindu philosophy (until they got “slapped down” by the Sunni).