I haven't done or tried this, but if I understand them correctly.... I believe Catalogs require that images be included into the catalog library (e.g. imported). In this case, I believe you would need to open the Catelog that you created, then import the folder(s) or file(s) that you would like to be included. However, this doesn't move files from their physical location to the location of your catalog - it only supplies the LR catalog with the location of the file(s). You can choose to export Catalogs to be used on other computers; useful when you import photos to your laptop, and decide you want to move the files + any edits in LR that you have performed to another computer (e.g. desktop). However, within a catalog you can create Collections of images from within that library.
I don't know if you are familiar with the Apple 'eco-system' [If you will] with regard to how iTunes works, but I understand it much better to think of how LR works in those terms. I can have music in many places on my computer, on various drives and in various folders. I can choose what files/folders to import into the iTunes library (a la Catelog); I don't have to import all of it. I can access any of these songs (only those which I've added) via iTunes. Additionally, I can create various playlists of my favorite songs (a la Collections). I can choose to put the same song into various playlists; simiarly to the way that pictures can be added to collections. In both cases (whether imported or added to collections) the files aren't duplicated (in terms of physical copies of data) they are simply linked.
If I am following you correctly, I think it would be easiest to import pictures into a specific catalog, then export the Catalog (including the actual files) to another drive. This assumes that you want to remove the pictures from your C drive. After exporting the Catalog, you would still need to physically delete the images from your C drive - after ensuring that exporting your Catalog worked properly.