There's no connection between Christian Science and Scientology apart from a few similarities and the superficial resemblance of the names. Christian Science was inspired by the New Thought movement of the mid-19th century, while Scientology was pretty much made up by L. Ron Hubbard in the 1950s as he went along.
Their founders were both paranoid and sue-happy toward critics. Their respective "theologies" deny the reality of the material world. But I think it's a coincidence that both are influential in Hollywood. Scientogy has promoted itself pretty aggressively to celebrities since the beginning; it was a way of buying credibility. Christian Science is an older American new religious movement that was pretty well established and respectable by the time of the golden age of Hollywood, and it seems to me its appeal was a bit more grassroots.
