The Project Manager is responsible for cost and schedule, the Project Engineer is responsible for technical content.

A project manager will help define the goals and objectives of the project, determine when the various project components are to be completed and by whom, and create quality control checks to ensure that completed components meet a certain standard.

 The Project Engineer bas the primary responsibility of producing a complete, accurate, biddable, and buildable set of plans for all the structures in a project. This responsibility should be performed with the least possible manpower expenditures.

Arvind, when in doubt, go Wiki the semantic meaning of the words you want to know about. You will only understand the concepts properly and in depth if you did the research your self. 

To assist with your answer. In general, engineering is the application of design principles and techniques. Typically, management is the organizational activities of planning, organizing, directing, controling, executing, and so on.

Project Engineering pertains to the application of a systems development life cycle to a specific project - using general systems-engineering principles.

I discussed PM at length in my paper on project management methodology. In short, PM is the application of management functionality to the project environment.

These 2 should maintain different perspectives of the project deliverables and its strategic environment. The one is the eagle, the other the hawk.    

Both engineering managers and project managers require managerial skill.  But they use different method. An engineering manager normally holds responsibility for managing a group of employees working for him.

A project manager typically manages a project, and not people directly. A project manager will often be responsible for gathering teams of people to accomplish a task. Once the project is completed the team is disassembled.