Respectfully, I don’t think you are completely correct.
While you are right that Kelvin is tied to absolute zero, it is also defined in such a way that a change in 1K corresponds to a change of thermal energy kT by 1.380649×10−23 J (the Boltzmann constant).
It is the difference in what 0K describes, along with the fact that a change in temperature equals a specific change in thermal energy (the measured value to which I previously referred), that separate it from Celsius. In Celsius, zero is the freezing point of (mostly pure) water (at sea level), and a change in temperature has no relationship to a specific/prescribed change in thermal energy.