Not sure but would relative pressure be a pressure relative to an absolute pressure, i.e absolute pressure "being that of space".. conventionally 0 Pa due to a void of particles..Although it does depend what kind of pressure you are talking about, space itself being is probably some form of energy resulting in a pressure "off" space. But i suppose that may beside the point.
In your case, in the test, i would say the reference pressure is with respect to a vacuum. If the atmospheric pressure is adding to the absolute pressure, then you would have to substract the atm pressure (101.3 KPa ) from the relative pressure in order to obtain the absolute pressure (with respect to vacuum). The absolute reference pressure may be directly measured with respect to the vacuum by creating a vacuum.
As for temperature, along the same lines i would say absolute temperature is temperature in kelvin, i.e with respect to absolute zero.
As for : Are they 1.01bar and 273+20K? These would be relative pressure and temperature, relative to a "standard environment".
May be wrong though..
Does that help at all?