While they can be the same bottle, the different terms mainly refer to how the gas is being used.
For Calibration, you may use a bottle as a part of a Calibration Kit which includes the bottle, regulator, tubing, and calibration adapter for the meter you are going to calibrate. When you calibrate, you are adjusting the values of the sensors in the meter that correlate to the concentration of the gases in your Calibration Gas cylinder. During Calibration the alarms are typically deactivated for a time period.
When you perform a Bump Test, you are simply applying the gas to the meter while in normal operation mode to confirm that the calibration has been accepted and the meter displays the gas concentrations (typically +\\- 10%) of that in your cylinder. This also verifies that the visual and audible alarms are operating properly. The Bump Test may also be referred to as a Functional Test.