I object to "warp core" in connection with TOS for two reasons. I think it's lazy - it's this way in TNG so it's always been this way! And it discounts any changes or advances in Trek tech. It's like calling the things on the wings of a B-17 "jets". Sure, it's propulsion and even a similar layout and position. But calling them jets is silly.
But really it's "keep your damn TNG out of my TOS".
I've been saying this for awhile. I assume TOS warp works on a different principle than ENT or TNG warp drive. The basics are the same but the way they achieve the "warp" is different.
Physical "warp generators" as opposed to cast coils for a start.