Confirmed by manufacturer Advanced Thermal Solutions, the main difference between these two parts is the thermal interface material used.
ATS-54170W-C1-R0 is T412.
ATS-54170W-C2-R0 is the exact same heat sink assembly with an equivalent thermal interface material (Saint-Gobain C675).
They are considered interchangeable by the manufacturer.
Here is the datasheet of ATS-54170W-C2-R0
Applicable part numbers