By default, favorites remember all the settings of the tool. You can choose to have favorites ignore certain settings; when a favorite is applied, those settings will be unchanged. This is called parameter exclusion. It is one of the favorites preferences, which you get to via the flyout at the upper right of the favorites palette.
Only a handful of parameters can be excluded. The exclusions are global: If wall height is excluded, it's ignored by all the wall favorites.
The exclusions, like the favorites, are stored in the file; but exclusions are not imported when you load favorites. (Or maybe they're not saved. Makes no difference in the end.)
This is a summary of the exclusions in our template:
• All elements: ID
• Wall & column: Height
• Section/Elevation: Name
To put it another way, these are the things that are allowed to vary as the favorite sets everything else.
Remember, favorites are nice, but option-clicking is often best. To make an element exactly like another, always option-click.