The 'Adam West Christmas Story' might be a personal account of Adam West's Christmas experiences. It could involve his family traditions, such as gathering around the Christmas tree, opening presents, and sharing a big Christmas dinner. Perhaps he also visited children's hospitals during Christmas in his Batman costume to spread cheer.
One key element could be the character of Adam West himself. Since he was associated with Batman, his heroic image might be central to the story. Another element could be the Christmas setting, with snow, Christmas trees, and presents. And if it's related to the Batman series, there might be some action - packed scenes against villains who try to disrupt the Christmas cheer.
One possible plot could be that Batman is facing a new and mysterious villain in Gotham. While investigating, he somehow gets transported to an alternate dimension where he meets Adam West, the iconic Batman from the past. They team up to fight crime in this strange new world that combines elements of the classic TV show and the modern Batman universe.
Family Guy is completely fictional. It's known for its outrageous and imaginative characters and situations that are not drawn from real life. The show is all about entertainment and comedy rather than being based on actual events.