A project administrator is someone assigned to the routine project management tasks such as running meetings, collecting status, and updating schedules. It's more a support role than a leadership role. They help the people who develop and continuously evaluate the plans. A PM or someone performing the PM role may have one or more administrators to help manage their own workload.
A tool administrator is generally an expert user in some tool, like MSP, travel reports, or whatever most people use only occasionally if ever. Program licenses can be expensive, and you don't need everyone to be an expert in every tool, if a few well trained users can manage that tool for everyone. Saving Changes...
Commonly I heard Project Coordinator for the role that Keith described as project administrator, usually they request a CAPM® certification.
I've never participated in a project or worked in a company, with a Project Tool Administrator, we have admis for the different tools that we have in the company. Saving Changes...
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