Yes that is correct but there are a few modern adaptations such as: Teach him how to fish, and watch him sit in a boat and drink beer all day. and Teach a man to fish, and make him a liar for life.
"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime" is, indeed, an ancient Chinese proverb. Most such things appear to have been coined by Confucius, though there is no specific evidence that this one was.