I am looking for some information about laser beam pointing stability
measurement.

Based on my search, two defintions of beam pointing stability are
being used.

1. Angular beam pointing stability: unit: angle/time or angle/
temperature, assuming beam is collimated, it can be measured by 1)
lens and beam profiler at focal point and 2) two beam profilers at
different location.
2. lateral beam pointing stability: unit: distance/time or distance/
temperature, it can be measured by setup 2).

I would like to ask if it is a correct statement and there is other
definition of the beam pointing stability.
I am curious which setup and definition are being used in laser
industry and what number is considered as good (1 urad/C or 10 urad/
C... ).

Angular stability is the most common one used. As to what is a 'good'
value, it mostly depends on what kind of laser is being used and its
actual mechanical construction. Some are inherently horrid and need the
end optics to be very close to the resonator and others are suitable for
propagation over very long distances. In general, the longer the
resonator the more stable it will be provided attention has been paid to
temperature stability.