Here are the definitions from PMBOK Glossary:

Project Life Cylce : a collection of generally sequential project phases whose name and number
are determined by the control needs of the organization or organizations involed in the project.
A life cycle can be documented with a methodology

Product Life Cycle: A collection of generally sequential, non-overlapping product phases whose name
and number are determined by the manufacturing and control needs of the organization.
The last product life cycle phase for a product is generally the product's retirement.

Project is the one which is executed to create a unique product or services and Product is the outcome of a Project.

The product life cycle starts with the business plan, through idea, to product, ongoing operations and product divestment.

The project life cycle goes through a series of phases to create the product. It generally defines the task to be accomplished in each phase or sub-phase and the team responsible for each phase defined.

Generally, a project life cycle is contained within one or more product life cycles.

Sincerely

CuongPT

PMBOK explains it nicely.

product lifecycle = project life cycle + maintanance + support