Release Management is the process which governs or manages the release of new or changed systems/services or products. These changes can be software, hardware, or a combination of both. Sometimes the development and subsequent release of the service/system components is organized in the form of a project.
Project Management is focused on the delivery of projects (which may or may not result in a release) within a defined scope, budget and timeframe. Release Management assists Project Management by defining the guidelines that each release must adhere to with regard to testing, acceptance, scheduling, securing code etc.
Although the Project Manager maintains control over the project itself, often the output of that project can be one or many "Releases."
By nature the project will definitely end, the releases, however, will continue to live on in the production environment as a system/service or as component of a system/service. In this sense, the project is the vehicle through which releases are delivered. Release Management is the "map" which describes the route to go from development to the production environment.
The project formalizes the effort and breaks it down into manageable tasks with resources, costs and timeframes assigned to each. Other times, releases are implemented through less formal mechanisms such as in response to break-fix activity, or as part of regularly scheduled maintenance activities. No formal project is necessary to carry out these activities.
Additionally, because Release Management takes a holistic approach to release, the process also considers the necessary levlel of training, communication and user/customer preparation necessary to deliver the defined level of quality.
Release Management can also define the procedures for each of these activities. These efforts help to provide a consistent set of standards that are applicable to all releases (including those that result from projects.)
By defining a standard set of procedures, Release Management helps to build "quality" into the process.
I've developed the following table of more of the differences between Release and Problem Management. (Click to download)