they do better/cheaper than anyone else, and trade for the rest.

This is absolute advantage. Comparative advantage is when a country can make something relatively cheaper then the other goods. So if a country A can make a coat for 10 tögrög and a bicycle for 20 tögrög, while a country B can make both for 30 tögrög, it means that the country B has comparative advantage in making bicycles and it would be more profitable for both if country B makes bicycles and trades for coats with country A.