The main difference between the two are that Henry VIII split from the Catholic Church for personal reasons, while Martin Luther wanted to transform the church because he disagreed with many teachings of the church.
King Henry VIII wished to divorce his wife, Catherine of Aragon. Divorce was not permitted by the Catholic Church. The king asked for a special request for a divorce, which was denied. The king ordered the Archbishop of Canterbury to grant him a divorce, which he did under pressure. England broke away from the Catholic Church after he was granted the divorce. The king then declared himself the head of the new church, the Church of England. Additionally, Henry VIII did hold some personal beliefs beyond the issue of divorce which conflicted with those of the Catholic Church.
Martin Luther questioned the belief that salvation could be found through the Catholic Church alone. There was also the threat of excommunication for those whose behavior did not align with the church, which Martin Luther also disagreed with. He did not think that one should pay penance for sins. He did not believe in the sale of indulgences. Martin Luther wrote about his condemnation of indulgences in his Ninety-Five Theses. Luther had to go into hiding due to the negative response from the Catholic Church.
When Henry VIII split from the Catholic Church, he was granted a divorce and given even more power. When Martin Luther protested some of the practices of the Catholic Church, he was persecuted and had to go into hiding.