What does "material finish" imply in heat-sink terminology?
It is literally how the heat sink material is finished after fabrication. Using your examples:


Anodizing a conductive heatsink makes it nonconductive. Use this if you want the part's case voltage isolated from the heatsink.
No finish would be raw material. If the heatsink is aluminum, it will come with no paint, completely bare aluminum.
If you intend to use a thermal paste between the part and the heatsink, a degreased finish, free from machine oil, would be a good starting point.  


This is an area where you really need to consider your application, and what you need from the heatsink.