Sometimes these two positions are at an equivalent level and sometimes a Program Manager is a more senior level. In either case, this position generally holds responsibility for a specific program or project, or series of programs and projects, with an organization. Most often, this position reports to the Executive Director or CEO, although sometimes there may be higher-level managers in-between.
Depending upon the size of the agency they may be responsible for supervising other staff or volunteers (including recruitment, hiring/firing, performance evaluations), monitoring budgets and financial accounts, fundraising/grant writing and overseeing the activities of a project(s). They may also be required to conduct project/program evaluation, review data and report on performance indicators.
A Project Coordinator/Program Manager is often an expert, or at least very experienced, in many of the job skills that their staff will need to have. This lets them understand the work that is being carried out by their staff which means that they are both able to fill gaps when needed and relate to the staff and volunteers that they supervise.