Centering Prayer, or Contemplative Prayer as it’s often referred to today, is nothing more than turning toward Christ who dwells within.
The use of a Sacred Prayer word, which is repeated when we become aware that we’ve been distracted away from prayer, is merely to be used like Hail Mary’s, The Jesus Prayer or other prayers just as saying the name of Jesus. It’s like a compass. It points us toward the focus of our intention,l which is being in the presence of God, who dwells within. St Teresa of Avila referred to this as “Mental Prayer.”
Centering Prayer, is Christ Centered.
Eastern Meditation is of course not centered on Christ, nor interior prayer itself, but seeks to transcend, outside of the self, hence the term, “Transcendental Meditation.” is often the term used.
The two methods have a different purpose entirely and should not be confused as being the same, even though the mechanics look alike.
Jim