‘Nature’ is the world conceived without reference to God. A natural rock is a rock as if it exists on its own or as part of a world that exists on its own. It has no absolute origin. Its only ‘origin’ is from other rocks, other existing substances. It is all transformation. This presupposes a metaphysics of materialism.
‘Creation’ is the world conceived as made by God from nothing & dependent on God for its continuation. Something of the nature of creation can be gained from the attributes of God. We can expect orderliness for God is a God of order. We can expect some reflection of purpose for God surely had a purpose in creating the world.
‘Natural history’ is history (conceived with reference to God and) with particular reference to the non-human world.
Creationists do not ‘add God’ to the natural world. There is no natural world without God. Creationists take off the blinders of naturalism that prevent the acknowledgement of the reality of God.
The laws of nature are conceived by naturalists as laws without a legislator. The laws of nature are conceived by creationists as laws created by God. They are laws of creation.
Naturalistic science is sometimes considered merely methodologically naturalistic because it avoids ontological commitments rather than affirming an ontological naturalistic universe. This is a sham. There is nothing to recommend ontological minimalism beyond an academic exercise. Moreover, the results of naturalistic science are presented as conclusions about reality, not merely conditional products subject to further vetting by others.
A naturalistic science needs to justify why there are not chaotic, non-causal events. It has excluded these arbitrarily. It promotes deterministic states arbitrarily. It is open from below, not above.