In the former case it is termed physico-theology, in the latter, ethical or moral-theology.
"The Critique of Pure Reason" by Immanuel Kant
The physico-theological or teleological argument is what is often styled the argument from design.
"The World's Greatest Books--Volume 14--Philosophy and Economics" by Various
Ray, his physico-theology, &c., 30, 31.
"Principles of Geology" by Charles Lyell