Contemplaive Prayer is what St Teresa of Avila described as “mental prayer.”
St John of the Cross described it as “interior prayer.”
The Catechism at New Advent which is from 1917, calls it “Prayer of Quiet.”
Today it’s called, “Centering Prayer,” or just “Quiet Prayer.” as the former brings up controversy for some.
Regardless of what you call “Contemplative Prayer,” it is not, “Contemplation.” Contemplation is a gift from God, which is infused or acquired, but it’s the gift given to those who open themselves to God and Contemplative Prayer is often the method many find as the most helpful. However, being Contemplation is a gift from God, He provides it according to his desire to the soul who is open to Him, regardless of the method of prayer they use.
Contemplative Prayer for myself is a deeper level of prayer where the soul is moved closer toward union with God through the experience of His transforming grace which is given through love.
“God can not be grasped, except through love.” From the Cloud of Unknowing.