I noticed that stabilizer codes and additive quantum codes are equivalent, but why? I am confused at the word "additive" since the operation of stabilizer genertors is multiplication.
A stabilizer code is also called an additive code, because it is closed under the sum of its elements.
The namesake is described on page 33 of "Stabilizer Codes and Quantum Error Correction" (link).
Additionally, additive quantum codes are the quantum version of additive codes found in coding theory.