Here's the breakdown:
* The Bloody Mary is named after the Virgin Mary: The drink is named after the Virgin Mary because of its red color, which is reminiscent of the blood of Christ. There's no connection to Mary, Queen of Scots.
* Mary, Queen of Scots was a real person: Mary, Queen of Scots was a real historical figure who ruled Scotland in the 16th century. She had a tumultuous life and was eventually executed by her cousin, Queen Elizabeth I of England.
So, while the Bloody Mary and Mary, Queen of Scots are both red in color, they're not related in any other way!