John Cassian treats the four different types of prayers listed in 1 Tim 2:1 (supplications, prayers, pleas, and thanksgivings) in this way:
Supplications- Praying for someone else who has personally sought contrition from those past or present sins.
Prayers- the Greek here is “vows”; so Cassian says that these prayers are those which contain our own vow to strip off the world and choose to follow God. It is not unlike saying, “God, I promise not to do _____ again. Give me the grace to be transformed.”
Pleas- General prayers for people; our hearts move out to them and we take those aches before the Lord.
Thanksgivings- Reflection upon God’s goodness in the past and the assurance of the hope we have in the future, we are confronted with the opportunity to believe God will move in the present, as well.
Joe Skillen 