"Natural Theology" was written in 1802. What new concept has arisen in the ID movement since then?
Information theory and computation.
Scientific evidence that may demonstrate irreducible complexity - that is the new concept.
Natural theology is a concept of theology (thus the name). ID has nothing to do with theology. Natural theology goes back much further than 1802 and Paley's book - Thomas Aquinas was big into this concept 600 years earlier.
Natural theology are arguments based on a deity. There is no deity in ID - other groups with theology as their root embrace ID in their effort to support the concept of deity but ID does not contain a deity - just evidence of design rather than evolution. If someone claims the "designer" of the irreducible complexity is God - that is their trip, but it not part of ID.