A person who expedites.
On the other hand,
An expeditor is someone who facilitates a process. It is a position or role found within project management, construction, purchasing and production control. An Expeditor may be mostly related to a Supply Chain related business. An expeditor's role is primarily to look at the requirement levels in the business and fulfill the demands by either rescheduling in or rescheduling out the delivery date on the Purchase Order. The expeditor is also responsible for making sure there is no line stopping situation for a business. The key metrics which an expeditor influences may be - Ontime Delivery, Cash Flow Cycle and Inventory Management. An expeditor needs to be assertive and needs to know the business at high contextual levels1
We can see the usage difference from the WP article on Expediting.
The -er suffix is used for the generic noun derivative of 'performer of the action' of expedite as usual: expediter:
To save these unnecessary costs and minimize potential risks, the supplier and customer may agree on the use of a third party expediter.
The -or suffix is used for the specific office/designation assigned with the duties of expediting in the specific business context:
… the expeditor makes sure that the required goods arrive at the appointed date in the agreed quality at the agreed location.