Both "sect" and "cult" are negative terms, and they are only used to speak about someone else's church or faith community. It's worse to be a "cult" than it is to be a "sect", but both are pretty bad.
Nobody ever describes their own church / faith community as a "sect" or a "cult". I've never heard anyone say, "Well, I'd better go, or I'll be late for the service at my sect," or "Our pastor gave a great sermon Sunday at our cult."
Everyone who uses either word uses them to describe groups about which they are negative. Neither word is used in an appreciative way. I've never heard anything like "The local sect had a nice carol service this year" or "Our kids really enjoy the Sunday School and youth group that our neighbourhood cult organises."
In terms of formal grammar, "sect" and "cult" are both irregular nouns; and they are declined this way:
- my "one true church",
- your "denomination",
- his / her "sect",
- their "cult".
For what it's worth, here's my own attempt at defining "sect" and "cult". I'm trying to make them practical definitions, and a fairly simple definitions. For each definition, please think of a church / faith community you've been part of, either in the past or the present.
Sect: Does / did your involvement in this group lead you to be more compassionate or less compassionate in your attitudes toward the bulk of humanity outside your group? If "more compassionate", it's not a sect. If "less compassionate", it probably is a sect.
Cult: Does / did your involvement in this group lead the people who care most deeply about you to worry about your well-being? If "no", it's not a cult. If "yes", it probably is a cult.