In qigong there are basically three or four types of breathing. The first is natural breathing. Observing this breath with awareness is one of the most beneficial forms of meditation. Other breathing techniques include the tonifying breath, dispersing breath, diaphragmatic breath, and reverse breath.
In meditation/neigong the following descriptions do not apply. For a scientific analysis (with references) of breathing physiology follow this link.
Tonifying breath: Longer inhale than exhale. Used to energize the body.
Dispersing breath: Longer exhale than inhale. Used to get rid of toxins and nervous energy.
After practicing diaphragmatic/dantian breathing for a number of years I thought I had the breathing thing down. But one of the first things I noticed about my breath when running is that I was still not taking a complete breath. The belly was filling up but the top lobes of the lungs were not. I was not getting the maximum amount of oxygen possible to feed the body.
Another interesting component of breathing is with regards to mouth vs nose breathing. Mouth breathing stimulates the fight or flight aspect of the nervous system. When this happens blood pools in the core of the body. As a result, less blood is flowing through the lungs to exchange CO2 for O2. Performance decreases. In contrast, nose breathing activates the rest and repair response of the nervous system causing more blood to flow through the body and lungs. Also the hormone response is more beneficial. (Source)