There are many different definitions of Configuration management (CM), as can be read at Brad Appleton’s website. I personally like the old and short definition by Susan Darts stemming from the 90-ies:
I like this definition because it implies a constant change of the system (evolution), but change in an orchestrated fashion (controlling), requiring distinct knowledge and teaching (discipline) to perform. Without change there is no evolution and there is no need for CM to control it.
The big difference with Project Management (PM) is that PM controls targets, resources and activities over the course of a project, while CM controls the changing system itself. The timespan of PM is a project, while the timespan of CM is the lifespan of a system which lasts until end-of-life (i.e. end-of-evolution) of the system. And when does CM start? Well, as soon as the evolution of the system starts to be controlled, which is at or before the start of a project.
So, CM starts before a project starts and ends until after the project has finished.