What is "company compensation fuel" and "pad fuel"?
Company Compensation Fuel
This is a term, which seems to be used by Korean Air. They define it on their website:

▶ Company Compensation Fuel
fuel to minimize abnormal flight occurred. Based on this, fuel consumption performance is modeled for a certain period of time, and based on this, the amount of fuel repeatedly consumed excessively compared to the flight plan is added.

(koreanair.com, translated by Google)
So this is fuel added based on the airline's experience (hence company) for typical fuel use on a given route.
Pad Fuel
I have never heard this term and Google also does not find anything related to aviation. Is it possible this was a translation? If so, could you add the original term and where you heard about it?