I'm sure that the caption labels are stored in the Normal template. Creating a new label prompts me to save Normal.dotm (because I have that option set). I choose to save. Exiting and restarting Word, I see the new label in the Caption dialog box. And if I rename Normal.dotm and let Word create a new one, the added caption label has been lost.

When you moved Normal to the other computer, did you make sure to put it in the correct folder? It has to be in the User Templates folder, as indicated by Tools | Options | File Locations.

__________________
Stefan Blom
Microsoft Word MVP

Microsoft 365 apps for business
Windows 11 Professional