The modes originated in Christian chant, and you asked for a practical difference, so here is an answer from a chanter's perspective.
First, let me regurgitate the theory, then I'll give examples, and my own commentary.
Authentic and plagal have the same tonic. Their cadences vary here and there, just like any song, but they always come back to the tonic. Their difference is not where their phrases end, but rather which corner of the scale they each prefer to be sung in.
Compare 'London bridge is falling down' with 'Mary had a little lamb'. Same key. Same scale.
But one's melody lingers on the fifth (
Lon-___ bridge __ ____-___ down), the other on the third (
Ma-__ ___ _ lit-tle lamb).
The general difference is threefold.
Authentic has a higher range usually from the subtonic to the octave. Plagal has a smaller range, or at least the melody does not deviate too far from the tonic: it is often between four steps below to the fifth above. These are not strict rules, but just a general observation of Gregorian chants. The boundaries can vary.
Height of the key.
Authentic-mode melodies reach high (relatively speaking) above the tonic to the fifth, the seventh, sometimes the octave or beyond. Consequently, the chant is best set in a lower to medium key.
Plagal-mode melodies reach rarely more than 4 steps above---and below---the tonic. Consequently, they can be set to a low-, middle-, or high- pitch key. This is especially important in performance-practice when shifting between modes.
Authentic-mode melodies spend a lot of time highlighting the perfect fifth. Plagal-mode melodies emphasize their third instead.
The term 'dominant' for the 5th scale degree developed from the authentic modal model, but in the plagal modes the 'dominant' is the 3rd. This is the single most characteristic difference that shapes the melodies into one mode or the other, certainly far more than range. You can think of it as the chief target note of the mode.
Sadly, teachers of modal theory rarely give examples from the genre that it originally came from.
I have given links below to recordings that I think demonstrate the modal features well.
The Protus - Dorian
Mode 1 (authentic), the Dorian
Mode 2 (plagal), the Hypodorian
- Both modes are in the Dorian / Aeolian / minor scale.
- Both modes are based on the D tonic.
(Actually, the Mode 2 recording is in the absolute key of E, but, hey, this is chant! Nobody cares about absolute pitch.)
But notice that Mode 1 lingers around its 5th (A), while Mode 2 emphasizes its 3rd (F). The Plagal rarely goes higher than the 4th (G) and has a lot of subtonic to counterbalance the meekness of its dominant on the 3rd, in contrast to the Authentic melody which adventures up above the 5th (A).
The Deuterus - Phrygian
Mode 3 (authentic), the Phrygian
Mode 4 (plagal), the Hypophrygian
The tonic of both Phrygian modes is E. Notice in Mode 3 how the voice tickles the 5th (B), highlights the 6th (C) and often settles mid-figure on the 3rd (G). It drops to the tonic only at the ends of clauses.
The Authentic Phrygian's dominant is the 5th (B), but it was raised to the 6th (C) in many parts of Europe near the end of the first millennium. I don't know why, but I suspect organum and harmony had something to do with it.
Hypophrygian mode, in chant, spends a lot of time closer to the tonic. Contrary to the common belief that Hypophrygian's dominant is the 4th (A)---true only in simple psalm recitation---, it actually spends more time on the 3rd (G), the 2nd (F), and the 1st (E), typical of Plagal tones.
For the Mode 4 recording, they even had to artificially drop the tonic drone down four diatonic steps because of dissonance with the flat 2nd. (It's a complicated story. Mode 4 is weird.)
The Tritus - Lydian
Mode 5 (authentic), the Lydian
Mode 6 (plagal), the Hypolydian
Authentic Lydian is major with augmented 4th, having its tonic based on F of the diatonic scale. Its dominant is again the 5th (C), as you can hear Lycourgos Angelopoulos shredding that note. Notice sometimes the 4th becomes an accidental flat, casting the chant into major scale.
Mode 5 rarely passes under the F, but Mode 6 Plagal Hypolydian dances around the F like a child afraid to stray too far. With its 3rd (A) dominating, the 4th (B) often becomes a diminished neighboring note (B-flat) by law of attraction, and so in practice Mode 6 is more often major scale than Lydian.
The Tetrardus - Mixolydian
Mode 7 (authentic), the Mixolydian
Mode 8 (plagal), the Hypomixolydian
Mode 7 and Mode 8 are found on the G. Dominants are once again 5th (D) and 3rd (B) respectively, but Mode 8 tends to emphasize the 4th (C) instead of the 3rd as an alternative dominant. The reasons for this are very complicated, and have to do with a medieval aesthetic taste for the upper note of the half-step.
Notice in all four cases that the Plagal is the same mode as the Authentic in every way except its preference for a lower dominant.
Gregorian chant evolved from an older simpler Roman system of chant and was only later adapted to the Greek 8-mode system. The melodies have many shared features and are not always easy to classify.
Likewise, the tonic bases of the modes---D, E, F, G---were not fixed. Plagals are sometimes written in the 5th key, e.g. Mode 2 in A minor, versus the standard D Dorian.
The hypothetical modes 9 (Aeolian), 10 (Hypoaeolian), 11 (Ionian), 12 (Hypoionian), 13 (Locrian), and 14 (Hypolocrian) never found a lasting place in church chant, for there was no need:
The accidental flattening of B in practice meant it was commonplace for Modes 1 and 2 to modulate from Dorian to Aeolian, 3 and 4 from Phrygian to Locrian, and 5 and 6 from Lydian to Ionian. Mode 8 even sometimes goes Dorian, but only for chromatic effect.
The idea that the Plagal modes are strictly one fifth above the Authentic modes is false. They do happen to be up there sometimes (see below). But Hypomixolydian is NOT equivalent to the D Dorian scale. It's equivalent to the G Mixolydian.
Remember, the 8 modes are a subset of the hypothetical 14, of which half are mere variations on the other half.
The "hypo-" designation is pretty meaningless, other than to say the Plagal modes tend to be under the Authentic modes.
In fact, in the Byzantine system of eight church modes, the relationship tends to be the opposite: Authentic modes are usually lower and shorter in range, while Plagal modes often soar above the 5th. (The reasons are due to changes over time rather than a prescribed model.) The appellation there would be "Hyperdorian".
In the Middle Ages, shifting from one mode to another was more based on gut feeling than on theory, at least initially.
Scale shifting. Sometimes, the chant would keep its key while the voice bumped up from Plagal to Authentic range or else added a flat.
Mutation. Other times, the cantor shifted out of mode into the same mode 4 steps up, effectively lifting the key to the 5th without tweaking the intervals.
Here are examples:
St. Hildegard of Bingen composed an antiphon in both Dorian and Phrygian, flattening the second. This one from the post-Gregorian period shows a growing taste in the octave note.
Angelopoulos starts this Mode 2 gradual on the D Dorian, then shifts into A Hypodorian. This shifting happens occasionally in the middle of chants, Plagal becoming Authentic, Authentic becoming Plagal, temporarily. The melodies always return to their original tonic by the end of the chant. This one is an exception.
Pia Mater Gratie
A two-part conductus composed, the lower voice in F Lydian, the upper voice in C Hypolydian (C major). The tonic tension between the two modes, despite their shared scale, creates a contrast that sends shivers down my spine!
There is so much more to modal/tonal theory than just ranges, intervals, and predilection for scale degrees.
Modal theory is 10% scales and scale degrees, 90% learning the right motifs to improvize. All the above is the 10%. That other 90%, which I didn't get to, is basically chant theory.
But it would take an entirely different level of interest---and a Stack question---to even start delving the details of difference in melody among the eight church modes.
Anyhow, I hope it gives you an idea how the modes work in their original context.
Source: Daily chanting, lots of reading