"Projects are done to create products" (I am considering services as end product too.).  In real life example, let’s say a company needs to launch a xPhone in a market.  There will be multiple stages in product life cycle of your xPhone i.e we need to conceptualize the xPhone fist, do research and development and enter into market to allow the growth and move forward with mass production. You are expected to support consumers too after its launch to market. Eventually demand for your product in market will decline and your company  will phase out the xPhone (and may start working on yPhone depending upon your company's budget).  We have following typical stages in product life cycle:

Stage1. Idea (R&D and Development)

Stage2. Growth

Stage3. Maturity

Stage4. Decline

Usually project management life cycle starts and finishes under stage 1. You can conceptualize that project life cycle is subset of product life cycle.  For Figure and/or see more go to my blog.

http://www.pmp360.com/product-life-cycle-vs-project-life-cycle