Chorus, Flange, Phase and Detune can produce similar results, but they are quite different effects:
Chorus is produced with one or more delayed signals, with the delay time varied by an LFO (typically around 20 mSec). These signals are combined with each other and/or the original. The result is harmonically related notches moving over the frequency response. Contrary to popular opinion, Chorus is not strictly the combination of detuned signals, however, audible pitch variation occurs as a result of fast-changing delay times, such as high LFO speed, high LFO depth or fast changing LFO waveforms. Cheap/old digital effect units (not the Axe-FX!) have delivered chorus effects by mixing detuned signals which can sound similar, but it's not the original authentic chorus effect.
Flanging is closest to chorus technically, but not tonally. It generally uses a shorter delay (under 10 mSec) and feedback to accentuate the high frequency response peaks and notches.
For detuning, combining signals with different pitch-shift amounts produces tone similar to a Chorus without the movement of a chorus LFO. You can add to this effect with a short, fixed delay as well (or instead).
All of the above use a time delay to produce their effects. Phasing is different: it combines a signal whose phase varies with frequency with a dry signal. The result is a small number of roughly equally spaced notches in the frequency response. These notches are moved over the frequency response with an LFO that varies the wet signal phase response.
Of course, the caveat with all of the above is that the Axe-FX offers many advanced parameters on its effects, which allows much more variation than was available on original effects, so the lines are blurred between some of these effects.
