C macros are text substitution, implemented in a separate less-expressive language (the C pre-processor).

Lisp macros access the input program fragment as structured data, and manipulate that using the same Lisp functions and data structures that you use for regular, normal Lisp code.

I think that both forms are technically Turing-Complete, but Lisp is more expressive. In particular, it's much more common to see Lisp macros that destructure and reform their inputs, where C macros tend to see their inputs as black boxes that can't be opened. The textual-substitution model of C also has some extra perils, because code fragments can be context sensitive (such as creating identifiers that are already in scope).

In both cases, Macros are well-defined "things" in the sense that they are thoroughly defined in their respective language documents, but in both cases they are not first-class language items because they don't exist at run-time.