What are differences between these positions in matrix organization structure?
There is no "Project Expeditor" in this question and it is not related with matrix organization structure.
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In the PMBoK Guide (Fifth edition) it is written following:
Matrix organizations can be classified as weak, balanced, or strong depending on the relative level of power and influence between functional and project managers. Weak matrix organizations maintain many of the characteristics of a functional organization, and the role of the project manager is more of a coordinator or expediter.
A project expediter works as staff assistant and communications coordinator. The expediter cannot personally make or enforce decisions.
Project coordinators have power to make some decisions, have some authority, and report to a higher-level manager. Strong matrix organizations have many of the characteristics of the projectized organization, and have full-time project managers with considerable authority and full-time project administrative staff.
While the balanced matrix organization recognizes the need for a project manager, it does not provide the project manager with the full authority over the project and project funding.
P.S. The Tobias's link also has a good explanation of these terms.
An expeditor acts primary as a staff assistant and communications coordinator and has no decision-making capability. A coordinator has some authority and some power to make decisions and reports to a higher level manager. Therefore the correct answer appears to be coordinator.