In case of centrifugal pumps, how to distingish between machinery vibration like from bearings / unbalance etc. and suction / discharge piping vibrations.

Use frequency analyses and measure various points and even on the piping when suspect. Not enough; add phase - still not enough; add modal.

As Sam, says, analysis. Look at the frequencies in your vibration spectrum. If they are pump/driver related then the frequencies will be multiples of your speed, impeller vanes etc. Any other frequencies are probably associated with resonance from either the attached piping or possibly the foundation plate.
Piping resonance and vibration is a common problem with pump installations. However this resonance has to be "excited", by the energy from the pump/product for example, before it will show.
To check your piping, stop the unit and do a "bump test" on it. Attach your sensor/pickup to the pipe and hit the pipe with a heavy, soft mallet. The pipe will vibrate and you can then see its resonant frequency.
Also make sure that there are no sharp bends close to the pump inlet/discharge manifold. These can also cause vibrations in the pump.

thanks. getting clear. one centrifugal between bearing pump pumping high molecular wt. liquid.pump bearings casing vib. in horizontal direction - 10 mm/sec pk i. e. on the higher side. vib. in other direction i.e. V & A are less than 4 mm/sec pk. dominant freq. is 1X only. discharge piping also vibrating at the same frequency of 1X in horizontal direction. I am not able to measure phase as pump can not be stopped to attach reflexive tape. pls confirm what to do.even if I am able to measure phase, what information we will get from it.