little hard to tell from your description, but you need to move your render files as well. Well, not necessarily, it depends on where you want them. You do want to define where your render files are located. I have to deal with this all the time. I have a couple projects that I bring home to work on (yeah, I know. I don’t have a life other than this). FCP sees the original and portable drive as two different locations even though they’re named the same (the OS can’t be fooled that way). So I have to relink everything, and define the render files as living on the portable when I open from the portable drive. As an aside I make the process smooth by using ChronoSync to make sure the portable matches the original drive, including all the project files and the render files. Makes my life easier.
Non-linear: all the time and nothing but.