I know that "to make a bed" means "to prepare, arrange the bed sheets for sleeping in the bed". But what about "constructing" and "assembling" a bed, say, by a carpenter? Is it alright to say "I work as a carpenter. I make beds and tables" or should I use another phrase/verb?
Make a bed is indeed ambiguous. But arranging the linen is a so much more common activity, within nearly everybody's daily concerns even if they don't do it themselves, that unless there is some specific context pushing it, the other meaning hardly occurs to us.