The Oxford English Dictionary thinks that they're the same and that's good enough for me!
The only difference is that a doctor might refer to 'the spine' or 'the spinal column' but it's unlikely that he'd ever call it 'the backbone' (if for no other reason than it's not a single bone).
I suppose that really they are interchangable terms used to refer to the same whole. The spinal column is the bundle of nerves etc which carry information to and from the brain about your entire body. This is protected by the solid bone and cartilage assembly we refer to as the spine and/or backbone.
"Spinal column" may refer to the nerves, but the word "spinal" is just an adjective meaning "pertaining to the spine", it doesn't mean the spine is a different entity from the backbone! You could just as easily (albeit clumsily) refer to "the nerves in the backbone".
The spine is a part of the human body, backbone is something that soldiers etc.. are supposed to show when facing the enemy or heroes when facing certain death in the hydras lair or whatever.