Talkbox and Autotune are completely different effects. In the former sound of an instrument is modulated through a hose in the singer's mouth, in the latter the frequencies of the singer's voice are digitally manipulated, yet for many people they sound similar. Maybe the similarity is the harmonic element that makes the whole thing sound like a musical instrument is speaking. What is the reason for this similarity? Do they relate to each other in any way if we model them mathematically?
The techniques you mention (and others mentioned in the comments, like a vocoder), all have one very distinct feature: they create a sound similar to the human voice (because of the harmonic content, specifically the formants) but (through design or choice) completely lack the natural vibrato (cyclic changes in pitch) and glissando (gradually moving from one pitch to another) that is typical of the human voice. The result is an unnatural, somewhat robotic effect.
The Talkbox and Sonovox work in a similar way: an externally created sound (by a guitar, synthesizer or any other amplified instrument) is introduced into the mouth and throat of a person, by placing speakers against the person's throat (Sonovox) or through a tube that goes into the person's mouth (Talkbox). The person can then change the sound by moving his lips and tongue, just like when speaking or singing. This changes the harmonic content (which frequencies are louder or quieter) but not the pitch of the sound. The result is a sound that combines the qualities of the original sound (pitch, volume) with that of the human voice (timbre). If you use a sound that has only discrete pitches, like a piano or a guitar played without any vibrato or glissando, the result is unnatural and robotic, because the human voice does usually not produce perfect, unmodulated pitch.
A vocoder does the same thing in a technological way. You sing or speak into it, and it will analyse the frequency spectrum (harmonic content or timbre) of your voice, and then use that information to filter another sound source so that its timbre resembles that of your voice. Again, the voice changes the timbre but not the pitch, so you get the same robotic effect.
Auto-tune is a digital technique that was developed to correct the pitch of recorded vocals. Initially meant as an inaudible fix, it is now often used with extreme settings that remove any hint of vibrato or glissando from the human voice, again creating the same robotic effect.