The breathing apparatus are of course connected: this is not as much an anatomically accurate advice as it is one of where to focus control for best results. A focus on the lower abdomen helps keeping the channels in between pliable for the communication of finely controlled pressure (pressure is force per area and the diaphragm has a large cross section). Of course there is no air touching the diaphragm. Maintaining the connection to the abdomen also maintains the resonance paths, giving a sustained quality to the produced sound.
Additionally, the throat should not feel like a constriction: essentially one aims for a feeling of connecting the diaphragm's action with the mask where the sound is emitted, with the throat being relaxed and not the principal source of either sound or air.
Anatomically, of course, this is a load of nonsense, but the visuals of that description help to avoid constricting your airways in places and manners detrimental to sound production and vocal health, and there are centuries of experience that thinking and teaching in those terms produces good results even if X-ray videos of good singers would be more scientifically accurate.