Read and Do = Read the action required, do the action required and then check that the required action has been performed.
Challenge and response = Buttons are pressed and actions performed, the checklist is read and it is confirmed by the other guy(gal) that things are where they are meant to be.
Who presses is the buttons is another matter entirely although I think it depends on manufacturer, history and culture (and if you have a former fast jet pilot in the crew).
PM