Typically, the overlap between the product and project lifecycle is the development phase of the product.  Within the development phase of the product, which is generally followed by the introduction, growth, maturity, and decline phases, you can have the full project management processes: initiating, planning, executing, monitoring, and closing.  The effort for each of these project management processes is impacted by system factors such as management elements, governance frameworks and organizational structures.  The similarities between the product lifecycle and project management processes include they are iterative and interchangeable, but the difference is what’s previously stated, the project management processes integrate into the product lifecycle.  A real-life example of these two cycles is the development of a video game.  All of the project management processes for the video game fit into the development phase of the video game.

With your project life cycle sometimes depending on the project planning will continue almost through the entire project.  It is important to also understand that defining and planning go hand in hand for the cycle.  A very important piece of knowledge to consider with projects and products life cycle is to plan then execute to prevent the wasting of funds.  Also, it is important to understand that the number of sales changes over time.  The product life cycle breaks down into projects where they have to manage projects to each other in relation to time. So for example, there is a project: Product A-research, project: product A design, a project: product A regulatory section, and a project: product A testing.  On the other spectrum, if I am understanding correctly, Product cycles can all have separate projects with similar products: for example- Shea Moisture's ethic line: product A: hair products, product B: soaps, product C: lotions, while product D: bath line. They are all separate projects with similar products. 

I think the area of overlap can be found in the Product life cycle's developmental phase. During this time, the Project is being conceived, and the Project manager is going through the Initiating and Planning phase. As the Product life cycle moves into the Introduction phase, the project cycle is preparing or in the early stages of executing the other project. The PM monitors and checks as the Product cycle start to leave the Intro stage and move into the Growth phase. The Growth phase is comprised of Monitoring and Checking while Execution is still going strong. Finally, the Project cycle's closing portion occurs during the Maturity phase of the Product cycle because the heavy work is done. The Product cycle continues past the Project cycle until the product goes into a Decline and eventual obscurity.