Yes, "squash" is the general term for most varieties of кабачки -- except of course for the type known as "zucchini".
The tiny little dish of rare and costly "заморская икра, баклажанная" in Ivan Vaselyevich Changes Careers was, I've read, "stunt-doubled" by кабачковая икра! (I would guess because the color looked more attractive on film.)