Both reveal a distinct way of praying to God.
The Catechism of the Catholic Church summarizes mediation as “a prayerful quest engaging thought, imagination, emotion, and desire. Its goal is to make our own in faith the subject considered, by confronting it with the reality of our own life” (CCC 2723).
In meditation the “mind seeks to understand the why and how of the Christian life, in order to adhere and respond to what the Lord is asking” (CCC 2705).
This type of prayer is frequently associated with the ancient practice of “Divine Reading” (Lectio Dvinia), where a person meditates on the truths found in the Bible.
It is a type of reflecting where one ruminates on the truths of life and discovers their personal role in the cosmos.
Contemplation, on the other hand, is (in the words of St. Teresa of Avila) “nothing else than a close sharing between friends; it means taking time frequently to be alone with him who we know loves us.” The Catechism reiterates this theme when it summarizes this type of prayer.
Contemplative prayer is the simple expression of the mystery of prayer. It is a gaze of faith fixed on Jesus, an attentiveness to the Word of God, a silent love. It achieves real union with the prayer of Christ to the extent that it makes us share in his mystery. (CCC 2724)
Contemplation might best be summarized by the phrase, “I look at him and he looks at me,” a description of prayer that “a certain peasant of Ars … used to say while praying before the tabernacle” (CCC 2715).
While both types of prayer foster a relationship with God, contemplation is where that love is expressed and realized.
Contemplative prayer is when we contemplate “Someone,” a person, God himself.
Perhaps it could be put simply, meditation helps us to know God and contemplation helps us to love him.