They can be used to mean the same thing, i.e. speed up. But they are pretty different in many ways. Expedite means to try to increase the speed of a process. You often hear it used in relation to getting work done more quickly. Example: "The factory manager took steps to expedite production." Accelerate just means to speed up. It's not usually done by one thing to another thing. For example, the gas pedal in cars is called the accelerator because it makes the car go faster. Gravity causes objects to accelerate as they fall.

Accelerate is when something goes faster but not necessarily relating to a specific process. For example: " the wheels on the bus started to accelerate." You cant replace accelerate with expedite in this sentence because theyre not really synonyms. Expedite pertains more to the process of something going faster. Example: "can you expedite building that bus?" Can you expedite the process of the build? Its similar accelerate, and accelerate can be used where expedite is but not the other way around. Think of accelerate as more the mechanics of something moving fast and expedite encompasses the whole process of something being done.

Expedite means to rush something or make it move quicker. Accelerate is the action of something speeding up, like a car.

The difference is usually in the context in which the words are used. Accelerate generally is used to refer to physical speed. For example: "I want my car to accelerate." Expedite usually refers to a series of actions someone wants to perform faster. At work, someone might say, "This project is taking too long. Let us expedite the process."