When Unity opens a Project, the Unity Package Manager reads the Project manifest (1) to figure out what packages to load in the Project. Then it sends a request (2) to the package registry server (3) for each package that appears as a dependency in the manifest. The package registry then sends the requested information and data back to the Package Manager (4), which then installs those packages (5) in the Project. Each Project has its own manifest which lists the packages to load as "dependencies" of the Project.

Adding a package to a project requires an update to the project manifest, to ensure the Package Manager includes the package in the list of dependencies. Although you can modify the project manifest directly, it's safer and easier to work with the Package Manager window, which manages the project manifest modifications for you.