Chinese cabbage is grown from "Cabbage Seed" available at any farmer for 685 wen.

All I ever get from "Cabbage" seeds is "Flowering Cabbage". Although, when in the ground AND in the Farmer Life menu it's called "Chinese Cabbage". Is it possible to get either cabbage from the same seed??

Not sure about those seeds, but there are a lot of useless cabbage seeds and some seeds can crit and give you different plants. I am sadly not familiar with those seeds.