Question

Are these Crains related to Western star Randolph Scott, a Virginia native whose birth name was Crane?

Answer 1

He was born George Randolph Scott. His mother was a Crane. There does not at first glance appear to be any direct connection. Whether there is a tangential relationship would take a lot more digging. There is nothing currently in the tree that shows a relationship between George Randolph Scott and James Crain

Answer 2

For the most part, those who spell their name "Crain" tend to have Irish, Scottish, or Isle of Man bloodlines.  Those who spell their name "Crane" tend to be English.

Of course, there are exceptions to the rule.  Some Cranes changed their spelling to "Crain" just so they wouldn't be confused with all their "Crane" cousins and neighbors (as in Connecticut and New Jersey).  It's doubtful your James Crain is of the same family as Randolph Scott but the only way to make sure is to completely fill out the genealogies of every Crane in the U.S.  And, trust me, that's not an easy thing to do.  :D