Straight answer - no idea!
Here's some possibilities: Most tuners "fire" on the largest amplitude partial, which is not a bad idea because that seems to be what our brains fire on, too. The largest amplitude partial is quite often the second, because we tend to pluck at 1/4 string length and so it gets excited more than the fundamental. 5 cents sharp on the second partial due to normal string inharmonicity would not be out of the question.
So: a) as the sound decays, the fundamental can decay slower than the second partial and the tuner will switch to trigger on the fundamental, which is why you'll occasionally see a tuner "jump" or be unstable on a single note.
b) Depending on the frequency response of the mic, one tuner might be firing on the fundamental, the other on the second partial, depending on which one is seen as the highest amplitude to that mic.
c) "Smart" tuners have enough processing power to pick the lowest frequency partial present, and will fire on that. It won't necessarily sound more in tune, though.
If you have a tuning fork, all tuners should read it the same, as there are no partials to fire on. If you pluck over the 12th fret (open string) you can be pretty certain that the fundamental will be the highest amplitude partial, and most tuners I've come across seem to be able to trigger on it correctly.
Apps like the old G-Tune show a spectrogram and indicate which partial is being used as the trigger. You can force it to trigger on a particular partial, if you want. Apps like AP Tuner will plot the frequency variation of each partial over time (which is of interest to piano tuners). So depending how fast a tuner triggers and how well it tracks, you may get a different answer. iirc, the human brain takes about 0.2 seconds to assign pitch, so ideally you'd want a tuner to match that.
More, I suspect, than you ever wanted to know about tuners....
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) I've only called one customer at 4am fumbling with my phone in the dark. "hows that Strat playing!?" 
