As your question implies 'pressurise' can apply to increasing the pressure of any fluid whereas 'compression' indicates a change in volume.
To illustrate; a typical industrial gas cylinder will be filled to around 200 bar and might have a volume of 100l at 1 bar that gas would occupy 20000l. Often this is as much about storing and transporting produced gasses in a convenient package (eg argon for welding) as it is using the stored pressure to do work.
An incompressible fluid on the other hand occupies almost exactly the same volume (disregarding changes of state) regardless of pressure so 1kg of water has a volume of 1l at 1 bar or 100 bar.
Similarly using the term 'compressor' for a category of machine distinguishes it within the more general category of pumps.
It is not unusual to use terms like 'pressurised gas' but, in very general terms, we talk about compressed air simply because it is produced by a compressor. The term also implies that it is available at (more or less) ambient temperature as opposed to air which has been pressurised by heating.
Similarly without any other context 'compressed air' tends to imply high pressure air used to operate air tools or similar pneumatic machinery or plant.