We have Vertical cooling water pump.For Monitoring vibrations,Motor NDE end have casing vibration and shaft vibration while Motor DE have shaft vibration .In Control room DE shaft vibrations are coming of order 390 microns And casing vibrations are of NDE of motor are of order 100 microns.

And from external vibration instrument casing vibrations of Motor NDE are of 98 microns which is matching with Control room but DE casing vibrations are of order 130 microns.but shaft vibrations are order of 390 microns
Pump is running normal no physical vibrations are observed

How to compare shaft and casing vibrations

Is it safe to run the pump.

Can there be problem in instrumentation
or what could be the reason????

When you try to compare shaft readings in displacement to casing readings in displacement the difference will be due to the vibration transmission path. The shaft displacement is measured relative to the motor bearing and the casing reading is measured relative to the earth (seismic). You have to compare the shaft reading, 390 microns to the bearing internal clearance to see if you might be rubbing. In addition, you have to know the frequencies generating the 390 microns.
Set your hand held to read in velocity and see how the readings DE and NDE compare.
Do you have bearing temperature? Look at the trend data.
Ask the motor manufacturer for vibration limits on DE and NDE levels.