Mary Queen of Scots was a Stuart, not a Tudor. Elizabeth had her executed because her claim to the throne was arguably stronger than Elizabeth’s own.
Mary QoS’s mom was Henry VIII’s sister, Margaret Tudor.
Her claim was arguably stronger by her advocates, no one else. Both were granddaughters of Henry VII -- himself illegitimate -- and Elizabeth was the daughter of a son, making her claim (plus the fact that she was wearing the crown) stronger. They were both Tudors from the standpoint of having those zero-to-sixty off with their heads genes.