How are a religious cult and a religion alike? They both involve worship of a supernatural power or powers (e.g., god or gods). 

All religions start as cults. To become a religion, a cult must long outsurvive its founder.  

Popular religions include Christianity and Islam. The Church of Latter Day Saints has long outsurvived its founder, Joseph Smith. It is now a religion. 

The cult of Peoples Temple (leader Jim Jones) and the cult of the Branch Davidians (leader David Korash) did not long outsurvive their founders. 

Some variants of a specific religion, such as Lutherism splitting from the Catholic Church, start as a cult and eventually become a religion. 

Other differences between a religious cult and a religion: Religions tend to be less secretive than cults, and money donated to a religion is less likely to go in the pocket of the leader. Also, religions tend to be generally viewed as legitimate, positive forces. 

Some religious groups straddle the border between cult and religion. You could put The Unification Church and Scientology in this category. They have not yet long outlasted their founders.

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