Star-delta Connection

One possibility is that the supply for the compressor is not resilient enough to go direct-on-line without dragging down the supply volts to other equipment on the same supply.

Another is that the inertia of the compressor is too large for the motor to get away on direct-on-line.

There may be other reasons, historical, for instance.

The only way to find out for certain is to ask your local, friendly, Electrical Engineer.

Possibly the start and stop frequency of the compressor, was the determining factor...

http://electrical-engineering-portal.com/comparision-of-direct-on-line-dol-and-star-delta-motor-starting

Why is there a difference in connection long as the motors have the same power,

Just because they have the same rating, doesn't mean that they are drawing the same power at any given time.

The compressor almost surely has greater rotational inertia than the pump.

The duty cycle might also make a difference. the pump may only turn on once and stay running for a long time, whereas the compressor starts and stops a lot during the same time period.

A frequent duty cycle with a reduced voltage start will create more rotor heating, shortening the life of the equipment. The time during which the motor rotor is turning slower than design stator speed operating at design frequency results in excess rotor heat.

There are some incorrect conclusions presented in this citation, such as savings on cable sizes. Ridiculous in normal industrial environments.

Depending on the type of water pump and type of compressor, the required starting torque for the equipment is likely the reason for the application of one of the other.

Perhaps you have a positive displacement pump, and a centrifugal compressor, in which case the starting application might make some sense. Otherwise I find it bewildering to see the application of reduced voltage starters for any modern electrical system, you add more clap trap and failure points than ever actually needed in a reasonably well designed power system.

Star delta reduces the current demand on the supply, but star connection reduces standstill torque a lot compared to delta - it could only be used on a relatively easy to start load.

It may be it was a standard compressor unit and the supplier did it that way because most customers do not want a heavy demand to upset their supply.

Possibly, your plant may start both motors together automatically and limits on your supply dictated a reduction of maximum demand.

Since you have not given your supply capacity and what other motors or other loads you have, this can only be a guess.