Meditation and Contemplaion have historically been used almost interchangeably. However, I think there's a case to be made for distinguishing them in the following way:
Meditation is the active use of the mind, reason, emotions and imagination is grappling with Christian truths - scriptural or doctrinal, scientific or philosophical. It's a very important part of our spiritual growth that we learn to meditate in a disciplined and constructive way.
In Contemplation however, we are doing something very different. We are learning to let go of our thoughts, still our thinking and quieten our minds, resting our reason, acknowledging but not engaging with our emotions and imagination. This is a spiritual exercise (askesis) which, like all exercise, requires disciplined repetition and a commitment to keep going. Jesus often withdrew from public mnisry to spend time with God. So we too must take time to just be with God. We can't say Jeuss was contemplating, or meditating, just that he was praying. But from earliest times Chirstians who have pursued a holy life have found that their prayers always lead them to the prayer of quiet, of silence, of contemplation. It seems highly likely to me that Jesus really knew how to sit silently with his Father - Jesus knew how to contemplate!
Centring prayer is simply about recovering in our own day something the Church generally forgets, or thinks should be left to religious orders of monks and nuns. Because there have, of course, always been contemplatives. On the other hand it's worth noting that some Christian traditions are suspicious of contemplation as being somehow distracting, misleading, or even dangerous.
But Contemplation is for everyone, and it's got nothing to do with how clever we might be!