Ask HN: Lisp eval vs. Lisp macros. Are they the same underlying concept?

Is my understanding correct that Lisp's powerful macro system stems from the ability to write the eval function in Lisp itself? From what I gather, Lisp starts with a small set of primitives and special forms—seven in the original Lisp, including lambda. I recall Paul Graham demonstrating in one of his essays that you can build an eval function using just these primitives. Those primitives are typically implemented in a host language like C, but once you have an eval function in Lisp, you can extend it with new rules. The underlying C interpreter only sees the primitives, but as a programmer, you can introduce new syntax rules via eval. This seems like a way to understand macros, where you effectively add new language rules. I know Lisp macros are typically defined using specific keywords like defmacro, but is the core idea similar—extending the language by building on the eval function with new rules?