Are you a former Aperture user? I ask because your question sounds like you expect Lightroom to behave like Aperture which can blur the difference between the library and the folders. If you have used Aperture this "managed" way, you can import photos directly into the library file.
Lightroom is different. It separates the library or "catalogue" from the photos. The catalogue is on one drive. But the photos are separate and can be located in folders on multiple drives. You are probably seeing these folders in Finder.
To resolve your SSD problem, in Lightroom's Folders panel drag folders from the SSD to the drive where you want them to be. Next time you import, be more careful in the Import dialog and ensure that the Destination is the one you want.
Are you importing from camera or card reader? You should be able to “Copy” to the 4GB drive in the right hand destination panel of the import dialog.
To move folder simply use finder and drag a folder to the 4gb drive. In the LR Library right-click (control click) on the folder name and choose “Update Folder Location” and navigate to the new location.
LR will update the catalog links and you can then safely delete the original folder from the SSD.
First off did you mean a 4TB drive? You wrote 4Gb which is extremely small, like a Thumb drive.
Also I don't think you are telling us the whole story. Does your iMac use a FUSION drive setup and you are using some add on utility to view files stored on each independent drive? Because a FUSION drive system/setup makes 2 separate drives, a smaller SSD and a larger standard rotating HDD, appear as one drive to OS X, Finder and the users of the computer.
This would explain why when you try to move files from the SSD to the larger drive they end back up on the SSD. The FUSION drive system/software is automatically placing them where that system thinks they need to be.
There is a method to break apart a FUSION drive setup so OS X, and the user, sees 2 independent drives and allows the user to pick and chose where files are stored.