Product = Project (Development) + Operations
To the extreme, Project/Development-stage is time-controlled, while Operations is resource-controlled.
Of course, both are overlaps, and "fluids"- in nature or alive i.e. they cross the boundary so called "budgets", in and out from boundary to the other.
Name-wise, it can carry a 'product name ex. SAP' or 'process name- ex. IT system development project', both are the same stuffs.
Product Lifecycle has 4 stages: intro, development, maturity and decline. X-axis is timeline, Y--axis say, as $ turn-over. You can preceive the first two as projects, the last two as operations. Both focus on managing one product.
We try to see a product as a living thing, what a creative idea!!!
Hope it is useful.