No, they are not the same. Mariah Carey and Mary Carey are absolutely two different persons. The one is the famous pop singer, while the other one is an adult film actress. See? Unfortunately, the less famous one apparently wants to make use their similar last name to earn a living.
Thus, Mariah is trying to stop the porn star from trade-marking her similar sounding stage name, claiming fans could get the two performers confused.
Mary, on the other hand, insisted with the trademark papers she filed earlier this year, saying "I'm ready to battle Mariah over this because I've been Mary Carey for a long time. It's kind of funny because I'm a porn star and I've been being myself for a long time. I think she's being silly."
Okay then who do you think will win the trademark battle? Mariah Carey or Mary Carey?