An empirical temperature is defined as linearly related to some specific property of a substance or system, such as its electrical resistance. So if we had a copper resistance thermometer and a platinum resistance thermometer and calibrated them at the ice and steam point, there'd be no reason to expect them to give exactly the same reading at some intermediate temperature.
Thermodynamic temperature is based, not on the property of a particular substance, but upon the universally applicable Second Law of Thermodynamics. To measure temperatures on this scale we have to have a theory which links readings (on say a gas thermometer) to the thermodynamic scale. It turns out that for gases at very low densities, the thermodynamic temperature ratio is close to the ratio of gas pressures.