Whether the sound is a "poo" or a "burp" does not make much difference. In fact, both burps and farts originate from the air around us. However, it is not the air we breathe in that causes us to fart or burp.
This air is the air we inhale with our food when we eat. The air we breathe goes into our lungs, but the air that comes with our food goes directly to our stomach and intestines. The air that enters the stomach is then reversed and comes out through the mouth as a "burp. Farting is when the air that has passed through the stomach is combined with gas generated in the intestines and comes out through the buttocks.