Detune is a special case of Chorus. Detune is essentially identical to Chorus when the LFO chosen for Chorus is a sawtooth wave.
The pitch change in the output of either Detune or Chorus (or any modulated delay) is related to the shape of the LFO (specifically, the derivative or rate of change of the LFO signal). Any portion of the LFO waveform that is a straight line will result in a constant amount of pitch change (or no pitch change if the LFO is a horizontal line over that portion). The amount of pitch change will depend on the steepness (slope) of the LFO waveform over that portion of straight line. Any time the LFO shape curves (is not a straight line), the amount of pitch shift will change and no longer be constant.
When a sawtooth wave is used as the LFO (as it always is in Detune), the pitch change is fixed and does not vary. It will sound like a stable signal at a lower (or higher) frequency than the dry signal.
A Chorus typically uses a waveform such as triangle or sine, which will cause the pitch to rise above the dry signal, then fall below the dry signal as the LFO waveform progresses. Some prefer this, as the "average" perceived pitch agrees with the dry signal.
With Detune (or Chorus with a sawtooth LFO shape), the pitch will either always remain above that of the dry signal, or always below that of the dry signal by a constant number of cents. This can cause the signal to sound slightly sharp (with positive Detune) or slightly flat (with negative detune). Using a stereo or dual Detune with one voice above the dry and one voice below is another way to reduce this perception.
The real difference between Chorus and Detune is that Detune adds an algorithm to smooth the audio at the discontinuity in the sawtooth waveform, so no pop can be heard. Set the Chorus block to use a sawtooth LFO and you will have a Detune without the deglitch algorithm, causing periodic pops.
You still get a "swirl' using Detune, but the sweep only travels in one direction, then instantly resets at the top or bottom of the sweep.