Thermal resistance unit
The only difference between them is the zero value (position of origin).
Notice that the difference between any two points is the same on both the scales.
So 1°C rise in temperature means 1K rise in temperature.
1 degree C is equivalent to 1 degree K.
See image:

The SI units of thermal resistance are kelvins per watt or the equivalent degrees Celsius per watt (the two are the same since the intervals are equal: Δ1 K = Δ1 °C).