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Some of the differences will depend on the agile methodology being used and the other roles and responsibilities that are assigned on a team. However, one of the biggest differences that appears universal to all agile methodologies is the concept of embracing change. In traditional project management, the scope of the project is defined and estimated up front, so changes to that scope (referred to as "scope creep") cause problems for the team.
Another difference lays in responsibility and accountability. In many traditional environments, the project manager is held accountable for the success of the project. Many teams operate under the "one throat to choke" rule, in which they feel it's important to have a single person that is held accountable. Agile environments operate in an environment in which the whole team is held responsible for the success or failure of the project.
Please let me know if you need any clarification. I'm always happy to answer your questions.