SAVE PROJECT creates a VPJ file. It tells VP where to find the source files and how to handle effects, transitions, etc. Apparently,, the file paths on the PCs differ.
To correctly use a project between machines, first load it fully to the timeline on the first machine.
Then click the 3-lined 'hamburger' menu at the top-left of the window. Click on FILE, then on SAVE PORTABLE PROJECT AS.
This will create a folder containing the VPJ and all source files. Copy that folder to the other PC, open it and double-click the VPJ file to load the project.
Do not simply SAVE PROJECT. Save PORTABLE project as.