Yes, you are correct.
The theory behind portable devices is that they contain a subset of your main music library.
Not part of the music here and part of the music there.
There should be a master library on the pc that contains ALL of your content.
We generally use smartlists in MC to determine what exactly gets sync'd from the main library to the portable device.
I reiterate, the songs on the ipod would be copies of songs from the main library.
You will need to get all the songs off of your ipod onto the pc that you want there. There are tools to do this that you can find on ipodlounge.com.
Once those files are on the pc, import them into the MC library.
Then I would initialize the ipod in MC. This will delete everything on the ipod and create a new index on the ipod.
Then use smartlists to select the files you want sync'd to the ipod.