Sect

From Wikipedia:

A sect is a subgroup of a religious, political, or philosophical belief system, usually an offshoot of a larger group.

The key seems to be that the offshoot rejects the beliefs of the original group, which is what caused them to “shoot off.” So the word “sect” really always have to include the qualifier of the original group – “a Christian sect” or a “Sunni sect” – otherwise it has no meaning. It’s a relative term.

Also of note:

While the historical usage of the term “sect” in Christendom has had pejorative connotations, referring to a group or movement with heretical beliefs or practices that deviate from those of groups considered orthodox, its primary meaning is to indicate a community which has separated itself from the larger body from which its members came.

I think this is somewhat true of English in general. We don’t ever say “sect” in a positive sense. It seems to always be used pejoratively, to indicate that some group is broken from mainstream (i.e. accepted) beliefs.