what is the difference in u-controller processor sampling frequency and the z-domain conversion sampling frequency?
OK just read your bold words and realize you know what you are doing but, be absolutely sure that what you say in bold is absolutely true. Anyway, my previous answer was: -


  But if I increase the sampling frequency of my system while using the
  SAME discrete transfer function that i just converted from s to z
  domain with a SAME conversion sampling frequency of 1kHz , the step
  response gets further faster.


Of course it does - the rate at which you sample is totally part of the transfer function. If you work out your transfer function at one sample rate and then change the rate, then the transfer function changes.

Basically, when you increased the rate of sampling and thought you were using the same discrete transfer function, you weren't.

If you were mimicking an integrator by using an accumulator, the speed at which you accumulate (sampling frequency) determines the rate at which the integrator integrates.