Historically, ‘garbage’ was specifically food waste, what we now would call ‘kitchen scraps’ or ‘compost’ if you live somewhere with a municipal composting program, or compost yourself. (Historically, ‘compost’ generally referred to the finished compost, rather than also the waste going in.) ‘Trash’ was other non-compostable refuse.

TL;DR Trash goes to the dump, garbage goes to the pig pen or compost bin