As far as I'm concerned, when you cause something to be done more quickly, you are expediting it; but I remember at the time of the high school's chemistry course I got familiar with another word, "catalyst / catalyzer" which was a substance which could expedite the a chemical reaction's process. Then I think these two verbs can be always used interchangeably. E.g. I'm sure the following sentences sound idiomatic and natural and they mean exactly the same thing:
- Whereas he has some friends in high places, I expect him to catalyze the success process.
- Whereas he has some friends in high places, I expect him to expedite the success process.
Do you confirm it?