What is a couch? How is it different from a bed?

The couch is the ancient "bed". Basically, the function is no different from the current bed. You can sleep and sit on it. However, it is much lower than the height of modern beds, and in some ancient times, couches could be hung in the air and lowered when in use.

The origin of the word "stay" is: when there are good friends or distinguished guests, the couch is lowered and used by the guests.

Modern people directly use the word "stay" to express where they live. It's an extended meaning.