The PMBOK guide defines the 5 project management process groups as follows

Initiating Process Group: Defines and authorizes the project

Planning Process Group: Plans the course of action required to attain project objectives and define the scope of the Project.

Executing Process Group: Integrates people and other resources to carry out the project plan for the project.

Monitoring and Controlling Process Group: Regularly measures and monitors the activities of the project so that corrective action can be taken when needed.

Closing Process Group: Formalize the acceptance of the Project and brings the Project to an orderly end