In short, it’s not different at all. Let us explore why. When a person marries, do they stop being a human being from that point? Are they simply husband and wife and not human beings any longer? Of course not! They can be two things at the same time. But now, let’s flip this logic a bit. Every married person is a human being. But not every human is married. Similarly, every Sufi is a Muslim, but not every Muslim is on the Sufi Path.
At the core, Islam is the most fundamental foundation that Prophet Muhammad (saw) preached to everyone. The rules of Islam apply to all Muslims, Sufi or otherwise. In fact, to communicate the importance of Islam (Shariah), Prophet Muhammad (saw) became a living embodiment of what any Muslim can and should follow. However, there were certain advanced esoteric teachings that Prophet Muhammad (saw) applied to certain individuals that were never meant for the masses. While these individuals were given this training, they still remained Muslims as there were no contradictions between the two teachings.
Take the example of following the Sunnah. Following some of the ways of Prophet Muhammad (saw) is not mandatory, yet some people make a point to adopt them. It takes them to a higher plane of devotion, but certainly, it does not deviate them from Islam. In fact, just the opposite.
Knowing all this, there may still be some confusion left. However, when we see someone who proclaims to be a Christian Sufi, Jewish Sufi, or Agnostic Sufi, etc.. These are rare occurrences that do happen but are not claimed to be in accordance with any Authentic Sufi Order whatsoever. One can never deviate from the criteria set forth in Islam and Imaan before following the path of Ihsaan (Tasawwuf). That said, there are numerous non-Muslim devotees of many Sufi Masters. However, their path to the creator is different than that of Muslims. Tasawwuf is Prophet Muhammad (saw)’s teachings to revive the heart (Dil Ka Jilaa) and to give ascension to the soul (Ruh Ki Parwaz). One doesn’t have to convert to take advantage of it. Just as one doesn’t have to convert to take advantage of a flowing river. Inner reversion and inner conversion is already part of Tasawwuf but not in the way people think. When a person pledges loyalty and love to another person, how can they remain the same ever again? Who knows where they are in their journey of Tasawwuf?