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Reading [1], [2] and this smartphone app[3], I'm getting different answers to the question.
The smartphone app is stating 427ly. [1] states approx. 700 ly, and [2] states approx. 724ly.
Even if I take [1] as the correct value, why does [2] state 724ly and the app stating 427ly?
Thanks
[1] - https://en.wikipedia.org/wiki/Betelgeuse
[2] - https://earthsky.org/astronomy-essentials/how-far-is-betelgeuse
Distance measurements for Betelgeuse are a bit of a mess. Solutions based on parallax would be ideal, but Betelgeuse has a rather large angular diameter at most wavelengths thanks to its extended envelope; optical and infrared observations usually fall in the 40-60 mas range (see Dolan et al. 2016 for a recent review), while radio observations show a disk of emission roughly twice that size (O'Gorman et al. 2017). The parallax is expected to be much smaller that the angular diameter, on the order of ~5 mas, and so it depends strongly on the choice of the center of emission.
One of the first decent parallax results was obtained by the Hipparcos satellite in 1997, whose astrometric measurements allowed comparatively precise measurements of location, parallax and proper motion for over 100,000 stars. Hipparcos measured a parallax for Betelgeuse of $\pi=7.63\pm1.64$ mas, corresponding to a distance of $131\pm30$ pc$^{\dagger}$. This is that 427 light-year number the app cited. The Hipparcos-only result was subsequently improved upon significantly by van Leeuwen 2007, who found $\pi=6.56\pm0.83$ mas, cutting the old uncertainty in half; this would correspond to a distance of 152 parsecs. If you're going to quote a Hipparcos result, this is the one to pick.
More recent results indicate that this value is likely too low. Combining Hipparocs data with multiple multifrequency radio measurements using the Very Large Array, ALMA and e-MERLIN (Harper et al. 2008, Harper et al. 2017) gives derived values of $197\pm45$ pc and $222^{+48}_{-34}$ pc, with the former barely consistent with the purely optical results (the latter value converts to 724 light-years). These groups note that the Hipparcos stochastic astrometric solution required the addition of so-called "cosmic error" or "cosmic noise" terms to individual position measurements.
The papers above note that the photocenter at both and optical radio wavelengths does not coincide with the barycenter, and may change on timescales of months to years. Therefore, extended, long-term observations would be necessary to reduce any photospheric "jitter" or other variations which could lead to variations in emission and thus astrometric fitting. Harper et al. 2017 proposed joint ALMA and Expanded VLA/Jansky VLA observations and mm and sub-mm bands over a period several years, but also suggested that this would require "a Herculean effort" to achieve, for logistical reasons (how many telescope committees would be inclined to commit that much time up front?). Perhaps interest in Betelgeuse's recent luminosity dip could motivate this sort of observation.
$^{\dagger}$Rob Jeffries makes the point that given the pretty terrible signal to noise ratios of many of these parallaxes (Hipparcos was in particular was bad, but none of the observations are amazing), it's not clear that you can really get good, meaningful uncertainties on the distance measurement from them via $d=1/p$. I agree; it's safe to say that the jury is still out on those, and any source that claims a distance and an error should give make that quite clear.
Current measurements give a distance "somewhere between 567 light years and 835 light years", with a "best guess" of 724 light years.
So wikipedia is being honest and saying "about 700". We really don't know any better.
Earthsky.org is giving the "best guess" value.
The app is probably using the distance measured by the Hippcaros space telescope. This value is generally considered to be an underestimate.
Another answer explains why we find it so hard to measure this distance: What will it finally take to accurately measure the distance to Betelgeuse?
Look at this article: https://arxiv.org/abs/1706.06020. Depends on studies distance varies and this is probably the reason of this discrepancy. For instance Hipparcos catalogue gives $131^{+35}_{−23}$~pc, assuming pc=3.26ly it gives $\sim$427~ly. More details in attached article ;).
We are waiting for results from Gaia mission, because at first it made parallax of fainter stars and very bright, as Betelguse will come next, but I don't know when, maybe it was measured already, but I can't find any credible information. They wrote in https://www.aanda.org/articles/aa/pdf/2016/11/aa29272-16.pdf
"The 230 brightest stars in the sky (G < 3 mag, loosely referred to as very bright stars) receive a special treatment to ensure complete sky coverage at the bright end"
