Why the unit families look different but mean the same thing
The coefficient of thermal expansion is fundamentally a reciprocal-temperature quantity. It may be written as per kelvin or per degree Celsius, because a one-kelvin temperature step has the same size as a one-degree Celsius step.
Engineering references also often rewrite the same quantity as micrometres per metre per degree Celsius or microinches per inch per degree Fahrenheit. Those forms make the small expansion rate easier to read in practical design work, but they still express the same underlying coefficient.
1/K = 1/°C
Kelvin and Celsius intervals have the same size, so the reciprocal coefficient is numerically unchanged.
1/K = 10^6 µm/(m·K)
Microstrain-style engineering notation for the same reciprocal-temperature coefficient.