the.com/sect

means A smaller group that has split off from a larger religious or ideological body, usually over differences in belief or practice.

from From Latin secta, meaning 'a way of life, faction, or party' — itself from sequi, 'to follow.' So a sect is literally 'the followers,' the people who went along with a particular leader or teaching. There's a popular folk link to 'cut' or 'section' (as if a sect were something sliced away from the whole), but that's a false cousin — the real root is about following, not severing, even though splitting off is exactly what sects tend to do.