Delta Debugging provided a name and a generic algorithm for something that people had already been doing, but they hadn't been calling it anything and hadn't formulated it as an abstract problem.
DD just removes stuff. C-Reduce does lots more, such as inlining functions, rewriting the class hierarchy, instantiating templates, ...
[1] https://www.st.cs.uni-saarland.de/papers/tse2002/tse2002.pdf