Looking at the words, I would guess that Autotune will fix wrong notes you sang.
While talkbox is just talking into a box which is made into 'singing'.
Short said: it's fixed singing vs. pitched talking.
Talkbox is something that 'vocalises' an instrument for want of a better word. Listen to the beginning of Generator by Foo Fighters - talkbox but used with the guitar, it's really a kind of instrument and is more to produce a distinctive sound than to make things in tune. Auto-tune on the other hand does exactly what it says on the tin, and I imagine it is used by more artists than you think, although much less subtly so that it still sounds like natural vocals rather than a talkbox/vocoder.
Autotune is a piece of software that listens to the pitch of the singer and shifts the pitch up or down based on which actual key (C D E F etc.) it's closest to. You can choose how "agressively" the software alters the pitch to find a balance between a robotic and a more natural sound. The more natural choice alters the pitch more slowly and dynamically (much like a real singer) while the robotic choice alters the pitch directly to keep it in perfect tune at all time.
A talkbox is nothing more than a box with a built in speaker and a tube which goes from the speaker into your mouth. This way, if you put the tube in your mouth, the sound comes out of your mouth and you can modulate the sound by moving your mouth the same way as if you were actually singing. Basically, it is an artificial vocal chord, as the sound does not come from your throat and out of your mouth, but from the tube and out of your mouth.
Now simply play a melody through the talkbox with a synthesizer, modulate your mouth, grab a mic and you got the talkbox sound.
That's Autotune. And it's actually THE track that turned Autotune from a helpful correction tool for terrible singers into a whole new sound producers purposely started using, even when the singer could actually sing in tune.