what is the difference between petition and desire?
Petition=to ask for desire=to want
A "desire" is what one feels (an emotion) whether expressed or not. a "petition" is one way of expressing a desire.
We definitely need context to answer that because petition and desire are not exactly synonyms, though they could be related in certain contexts.
Similar words, but petition could be used in a legal proceeding, such as a petition for divorce, or to petition the court or to get a petition signed to change a law. It is more formal. In praying, we petition the almighty God. I would not petition my equal or someone in a lower status.
Desire would not be used in a legal context. It is a more personal word.
Maybe a distinction is that, for example, if I desire you to do something, I might be in a position of power. But if I petition you to do something, then you are probably the person in power.