"Denominations" of a religion would be separate religions that view each other as "variants". Like the Baptists and the Methodists. They're both Christians, but they're not the same organization at all. They are not sects of the same religion.
Indeed, which is my response to the example given
If you are an elder member of a religion, you can start a cult. Cults are sub-groups of a religion.
for example: a religion called Christianity could have 3 cults: Protestantism, Roman Catholic Church and Eastern Orthodox churches
So the religions are based on the same ideas(or at least have some ideas in common) but aren't the same. Other possible cults could be a group of 'mostly' infiltrators which act based on their believes but not always communicate with the religion.
Denomination - a group of religious congregations having its own organization and a distinctive faith.A Christian denomination is an identifiable religious body under a common name, structure, and doctrine within Christianity.
Sect - a subdivision of a larger religious group.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.
Cult - 1) A religion or religious sect generally considered to be extremist or false, with its followers often living in an unconventional manner under the guidance of an authoritarian, charismatic leader.
2) A system or community of religious worship and ritual.
