The primary role of a product manager is to focus on the product direction by establishing the product roadmap and vision. This role solicits requirements from customers to help define the release deliverables. In a more agile model, this role will continuously solicit requirements from customers to ensure that the release is an accumulation of deliverables that the customer actually wants (based on changing customer needs and market conditions). This includes identifying customers who can validate their needs either in an end-of-sprint review (if they are more agile based) or in a user acceptance test (UAT) if they are more waterfall-based. In addition, the product manager will focus on acquiring the appropriate funding for product development and participate in the marketing of the product.
In a more waterfall lifecycle, the product manager is not involved in the day-to-day tasks of a project release but in a more agile lifecycle, the product manager would participate more regularly in activities such as sprint planning and end-of-sprint review. The product manager may be involved in the high-level coordination of dependent product items with other product managers to get buy-in to ensure the other products will be available.
Because the role of release engineer often gets confused with the role of the release manager, a special focus on the release engineer role is included. The release engineer is primarily focused on the build, package, and release responsibilities focused around project deliverables. The release engineer role is fairly technical and focused on utilizing compilers, continuous build technologies, development technology build mechanisms, the ability to establish build processes, understand parallel and continuous build concepts and how to implement them. They also tend to be focused on packaging the build deliverables and migrating them through the remainder of the release lifecycle into production. This includes the ability to automate the process of packaging of the build deliverables, database deliverables, and other deliverables needed to establish a run-time testing environment into a release package or the skills to perform this task manually and the ability to automate the migration process to production. So you can see that the release engineer role is fairly technical and focused on the back-end of a project lifecycle getting the deliverables into production.
In some cases, a separate role of build engineer will focus on building and packaging a release and a release engineer focuses on migrating the release through test and into production whether that is installing the deliverables onto a production server or creating the master media by which duplicate copies can be made available.