The words are very similar and can often be used in the same way. Accelerate is often used in a more literal sense to mean changing the speed of something – for example, "I am accelerating the car". Accelerate can be used in a metaphorical sense as well but it seems to be a bit ambiguous. For example: "I am accelerating the project". This is something native English speakers say occasionally but it leaves unclear exactly what is being accelerated. It becomes clearer if one says "I am accelerating the pace of the project" but this sentence sounds a bit clunky. Expedited is often used in formal settings – jobs, government policy, etc. "I am expediting the project" does sound a bit more formal than "I am accelerating the project" but I think it makes very clear that somebody is trying to complete the project ahead of schedule. "Expedite" is a great word to use in these contexts but keep in mind that it is rather formal. I hope this helps! I will think more about how the words are different. If I come up with anything, I will edit this!