Water is incompressible, which means that you can't squash it to make room for air. Air is compressible, which means that you can compress (or squash) the air and add a little bit more air.
One bottle is entirely full of water – you can't blow air into this bottle.
The other bottle has an air gap at the top. You can actually see the air bubbles going into this bottle. This increases the pressure inside the bottle.
This is a recommended pre-visit activity for a field trip to Science World at TELUS World of Science. It is related to exhibits in the Eureka! Gallery.