The proper English usage of those terms makes them interchangeable.
christianity is a cult, for example.
Look at MERRIAM-WEBSTER's definition:
Definition of cult
1 : a religion regarded as unorthodox or spurious - also : its body of adherents
2 a : great devotion to a person, idea, object, movement, or work (such as a film or book)
b : the object of such devotion
c : a usually small group of people characterized by such devotion the singer's cult of fans The film has a cult following.
3 : a system of religious beliefs and ritual; also : its body of adherents the cult of Apollo
4 : formal religious veneration : worship
5 : a system for the cure of disease based on dogma set forth by its promulgator health cults
christianity fits all 5.
1. tens of thousands of children raped in its churches. pretty goddam unorthodox!
5. many of the morons think praying will heal them.
And, you only need ONE of the above for it to be a proper usage of the term.