They are not the exact same thing, through similar. Let me put it this way…
Say you really need to find a job. And you believe that helping others in a justifying thing to do for God. Therefore you pray to God for others instead of for yourself, but your intention is to do this inorder for God to help you find a job. That is intention.
Anytime you begin prayer for a specific reason, it’s your intention. For instance, if you pray the rosary for the people down in New Orleans, that’s intention, not necessarily petition.
Petition is when you directly ask God, Jesus, Mary, or the Saints for help or guidance. Consider it a plea for help, mercy, or a sign. If you ask Mary to pray for those in New Orleans, it is a petition.
Does that make sense? I might have just complicated it, lol.