Yes the two Queens named Elizabeth are related. However, Elizabeth II is not a descendant of Elizabeth I, as Elizabeth I did not have any children.The two queens are first cousins, 14 times removed....
Upon her birth in 1926, she was not the heir to the throne. However, after he grandfather died (George V) in 1936 and her uncle (Edward VIII) abdicated after only 8 months as King she became the heir...