What is the difference between ''The Project Management Life Cycle and the Project Life Cycle according to PMI'' ?

project life cycle starts with initiating and it will be ended by closing.

initiating- executing- controlling and monitoring- closing

Project Life Cycle

• The project life cycle (which we prefer to call project life span) is a span of time from the project start to the end.
• In the SUKAD CAM2P™ model, the project life span covers the whole project from the idea statement to project closure.
• For most projects, this life span is divided into phases / stages. Each phase has a purpose, like a design phase, a feasibility phase, implementation phase, testing phase, etc.
• These phases could have different names based on the organization and industry.The Project Management Institute (PMI) is a leader in credentialing project management professionals and advancing the field of project management. The PMI has a global footprint in nearly 200 countries around the world. From its global headquarters in Newton Square outside of Philadelphia, the Project Management Institute provides certifications for project management professionals, as well as career training and educational resources. The group also maintains research programs to advance scientific and practical abilities within the industry.

I agree with Eng.Ahmed's answer