Does this DC pump and similar ones output at different rates or at one constant pressure/air flow rate?
The diaphragm pump displaces a fixed amount of volume per cycle. Increasing the voltage increases the number of cycles per second, so normally the flow will increase when you increase the voltage. However, the flow and the pressure depend on each other. If the flow increases, the outlet pressure also increases (more gas/liquid is being forced into the rest of the system). If the outlet pressure increases past a certain point, the pump also won't have enough force to push the flow.

So using the pump by itself, you can't normally keep the flow constant and just change the pressure. Nor can you keep the pressure constant and just change the flow. You need to add a flow regulator if you really want to keep the flow constant, or a pressure regulator if you want to keep the pressure constant. On the other hand, if you can tolerate variations in the flow, you can fool around with the voltage and try to get the pressure you want. Same for trying to get the flow you want, if you can tolerate variations of pressure.