What was the relationship between Charlemagne and the pope like

Pope Gregory IV didn't get along at all with King Henry IV. They did not approve of each others ways of ruling and religious teaching styles. They convinced each others closest and faithful servants to overthrow or remove one another from their standing position. Eventually, they forgave each other and popes and kings were then on known to have disagreements with each other and have a massive compromise.

There is no differentce in it