It's seem's to me that a project coordinator have to coordinate many professionals or institutions or something else. It's not obligatory for a project manager. I was a medical coordinator in a network and have for example to be sure that information is ongoing between all the professionals.
I am a coordinator of more than 80 projects. My work start from there when a project manager get struck because I coordinate between my department and the ministry to get different approvals because I know the methods of approvals. After getting I know how to get budget for project manager and coordinate between civil work, procurement and stakeholders. Very diff from project manager
Project Manager is essentially responsible for the planning, execution and closing of a project. He is overall accountable for the Project Delivery and to ensure that the key objectives of the project are delievered.
Project Cordinator is like a right hand of Project Manager, who facilitates the Project Delievery. He is the person who control all the project activities under the ditrection of Project Manager.Eg Chairing meeting meetings,controlling cash flows,tracking project progress, maintaing varios project logs, informaing managment about progress, ensuring communication between various teams etc.
This is from my knowledege during PRINCE 2 practiontioner certificate and my experience working in IT companies.