A confusion on two single-ended measurement systems
Why in RSE case there is potential difference between AIGND and
  measurement system ground?(Why this wouldn't be an issue in NRSE
  case?)


Seperate grounds will be at different potentials - this is a fact of life unless you are making a measurement to a device up-close to the acquisition system. Earth currents are the usual culprit in an industrial environment - current flows thru earth and creates a volt drop. This produces a measurement error.

If you have an NRSE system you can remotely measure the ground reference point directly and because no current flows down this extra wire there is no measurement error caused by earth currents.


  Why would one use RSE if NRSE would introduce less offset?(Does NRSE
  has some other disadvantages?)


NRSE can only work over a limited range i.e. it can only cope with a few volts of offset between measurement ground and acquisition ground.

Just to show you that a little bit of time put into both questions and answers (as well as trying to learn from answers) is its own reward, here's a picture and a simple (hopefully) explanation: -



There are two sensors labelled V1 and V2. They share a common ground connection back to the measurement device. They also share a common 5V excitation voltage (power supply if you wish). Sensor 1 takes 1mA whilst sensor 2 takes no current. The cable return back to the measurement device has 0.1 ohms in the 0V return wire. This will inevitably drop 100 uV due to the 1mA flowing. Even though sensor V2 is still producing 2V with respect to it's local 0V, the measurement device measures 2V + 100uV. 

Now if the measurement 0V were seperated from power 0V then the measurement system would measure exactly 2V.