In Silent Prayer, We Let Thoughts Go… Even Holy Thoughts?

A reader writes,

Hi Carl. I have a question that I can never find a clear answer to. In Zen meditation, one is to sit silently, and if thoughts come into your head, let them just drift away rather than focus on them, etc. “A flying bird leaves no trace.” I understand all that. Now, how does silent prayer differ from that? Yes, I don’t want to focus on monkey-mind thoughts of work, money, the bad weather, whatever. Let those simply drift away. But what about thoughts of God, Jesus, Mary and Josep...