How were church courts and manor or royal courts different from each other?

I think the first thing to consider is the Word 'court' and what it implies. Originally a royal court encompassed the hierarchy from king or queen down through the nobility and royal advisors surrounding the monarch. It also had a legal significance in that the monarch was the highest authority in the land and any lawbreaker or felon could be summoned before the monarch's court for justice. By mediaeval times, the Church had fashioned their heirarchy in a similar way: the pope, and the hierarchy of clergy including cardinals (who are still called princes of the church), archbishops, bishops and the various levels of authority down to simple parish priests and monks. The Church also had developed a legal system based on Canon Law. The authority of Canon Law is drawn from the Christian Scriptures and the long held belief in the Tradition of The Church also known as The Magesterium. Those who transgressed the laws of The Church could be summoned before a court composed of high clergy. Their final judgments and punishments could be swift and brutal including imprisonment, torture, and death, including burning at the stake. It should also be remembered that the Church considered their authority higher than that of the monarch because God's law surpasses earthly law. The principal church (cathedral) in any city in England and across Europe became a 'fortress' or place of refuge where civil law ended at the cathedral's entrance. Historically, Notre Dame Cathedral in Paris is arguably the best example of such a 'fortress'.