To be honest, it depends on the service. In my congregation, we always have a "moment of silence", which is preceded by a pastoral meditation or pastoral prayer. The meditation/prayer is usually delivered by the minister, but during lay-led services it will be delivered by a Worship Associate or other community member. Often "Source of Love", "Spirit of Life" or other, more inclusive terms are used to refer to the divine, rather than the trigger-word "God" which so many of us are uncomfortable with. The pastoral prayer may at times lean toward the Protestant side of things, in which we are clearly directing our attention beyond ourselves and our community to a greater divine reality. At other times the pastoral meditation will focus upon humanity, the "web of life", or other communities rather than upon something supernatural. It really just depends on the theme of the service and the needs of the congregation.
I should add that this part of the service also usually includes "joy and concern" cards in my congregation and quite possibly in others as well. The minister or service leader will briefly mention the joys and concerns (births, graduations, deaths, illnesses, etc) that members of the congregation want to share with the community, and then entreat us (or the divine, depending on the service) to pray for them, keep them in their thoughts, wish them strength, share in their joy, etc.