Within Revit parameters by default are unique. They are not identified by their name, but by a unique number, a Globally Unique Identifier (GUID).
So a parameter called Greenstar Material in a joinery (casework) family is completely different to a parameter called Greenstar Material in a piece of furniture.
You will notice this when you create a multi-category schedule. There will inevitably be multiple parameters that have the same name.
But sometimes you want to use the same parameter, perhaps you want Greenstar Material to be the same parameter for not only casework and furniture, but also doors and windows.
You also may want a parameter to appear in schedules, and/or tags.
You do this in Revit by creating a Shared Parameter in a Shared Parameter file.
Example line from Shared Parameter file:
By placing the parameter definition into a file you can share that parameter between different Revit categories, and even different Revit project files.
But remember the Shared Parameter file is only a container you get things from. Once a shared parameter is loaded it exists within the family or project.
When created parameters are case sensitive - Comment is not the same as comment.
If you delete a shared parameter and re-create it with the same name Revit will treat it as a new parameter (as it has a new GUID).
You can not rename a shared parameter once created.
There is not a live connection between loaded shared parameters and the file it came from. Deleting it from the file has no effect on families or projects it has already been loaded in to.
You can load shared parameters from multiple shared parameter files. But be aware parameters with the same name from different shared parameter files will be different parameters in the family or project they are loaded into.
A standard shared parameter file called SharedParameters.txt can be found in ...:\Revit Settings\Shared Parameters.
Look in this first to see if you can find the parameter you need.
If you can't find one DON'T CREATE A NEW ONE.
Instead create a new Shared Parameter file for you project and add it there.
The Shared Parameter file is a text file created and edited via the Manage > Shared Parameters command.
When adding a new parameter you can select a Shared Parameter by picking the Shared Parameter radio button.
A comprehensive explanation from AECbytes