If you have the 'FUL' message displayed on the LCD screen, it does mean that there is no more memory available on the SD card. If you don't have any files on the SD card, it's likely that some 'ghost' data is taking up the space.
If using a Mac computer, when deleting files from your SD card you must empty the trash before removing the SD card or unplugging the camera. If you do not empty your trash the photo and video files will not be completely erased from your SD card, and will still be taking up the memory. To completely clear the memory, you will need to reformat the card using your computer or the delete all function in the settings menu of the camera.
To delete all files and format the SD card using the camera, press the shutter button when 'ALL' is displayed on the LCD screen in the settings menu. 'ALL' will start blinking as a warning. If you then press the shutter button while 'ALL' is blinking, you will format the SD card, erasing all files and data. The red LED on the front of the camera will blink while the card is being formatted. Once the red LED stops blinking, the reformat has been completed.