Recently in another thread I was asked if I could elaborate on the difference(s) between tonal and modal chord progressions. I’ll try to do that here, but instead of doing a purely theoretical comparison, I’ll give you actual musical examples that you can play. I think this will help.

The word “modal” is unfortunately ambiguous, which causes a lot of confusion. But if we talk about contemporary modal music, then we cannot just consider harmonic progressions, we also need to look at the melodic aspects. In fact, originally, modal music was almost exclusively melodic; harmonic considerations came later (and obscured the whole topic quite a bit!).

In the examples below we will look at three (original) song fragments, each with its own melody and accompanying harmony consisting of only three chords: Dm, C and G (or G7).
The guitar will always be very simple and notated in tablature. The melody will be in standard notation only; but even if you are not fully comfortable with standard notation, you should have no difficulties reading it.

Example 1

The empty key signature suggests the key of C major or that of Am. Since the melody ends (and insists on) the note C, we obviously go for C major: C D E F G A B.
As you can see, the harmony progresses in fifths, i.e. the roots of the chords progress by intervals of a perfect 5th. This is usually a strong indication that we are dealing with a tonal progression. The cadence G7 -> C (V7 -> I) confirms this. There is also more emphasis on the C chord than on the two other chords.

At the melodic level, we seem to have three phrases: the first one goes (down) from D to G, then from B up to C, and finally from D to C. So the long range targets of the three phrases are globally compatible with the natural melodic tendencies within the C major scale; moreover, we find two very conclusive B -> C melodic cadences.

In summary, this is a purely tonal song in C major, as you probably expected. We analyse it as
|ii |V7 |I |% |. This is as tonal as it gets.

Example 2

The key signature is empty again, but this time the song doesn’t end on a C: the note C at the end of the 4th bar is a passing note that actually resolves to D in the first bar. Moreover, the Dm chord is emphasised more than the two other chords. Also note the lack of typical C major cadences (B -> C at the end of bar 4 is NOT a cadence since we don’t resolve on C).

Melodically, we have two phrases: the first one goes from D to D and stresses the notes D and F; the second phrase goes from C to C and stresses the note B. As mentioned above, the final C is a passing note towards D. That D note really feels “home” and suggests D Dorian.

The signature of the D Dorian mode (D E F G A B C) is (1, b3, 6) = (D, F, B) and as said, these three notes play an important role in this melody.

So D Dorian is confirmed and we analyse the progression as |i |% |bVII |IV |.
The notation may look weird to you. When dealing with modal harmonies, we conventionally notate the chords in reference to the corresponding major key.
In this case, the corresponding major scale is D major: D E F# G A B C#, and the chord family is
D Em F#m G A Bm C#° = I ii iii IV V vi vii°.
The D Dorian chords are Dm Em F G Am B° C = i ii bIII IV v vi° bVII (when compared to the major chord family).

If there was no melody, you could arguably interpret the harmonic progression as
|ii |% |I |V | in C major with a half or interrupted cadence, even though it would be relatively awkward. But with the melody, this possibility is completely removed, particularly if you actually sing and play the “song”.

Could this be D natural minor? No, because the Aeolian mode has a b6, not a 6.
Could this be D (harmonic) minor? No, because then there would be a #7 (C#).

Example 3

The main chord here is G (and even G7!) and there are no typical tonal cadences suggesting that this could be G major or C major.

Melodically, we have four phrases: the first one goes from G to G, the second one goes from F to D, the third one goes from C to G and the last one goes from F to F. Again, the last phrase actually resolves to G. All this suggests G Mixolydian.

The signature of the Mixolydian mode is (1, 3, b7); the melody in this song insists heavily on 1 (G) and b7 (F), and the harmony provides the 3 (B) in the G and G7 chords.
So we are definitely in G Mixolydian. We analyse it as |I |v |IV |I7 |.

It would make very little sense to analyse this song as |V |ii |I |V7 | in C major, even without melody.

Conclusion
Tonal music is characterised by strong melodic cadences (leading tone to tonic and subdominant to mediant) and harmonic cadences (V -> I, ii -> V -> I), and the long range melodic tendency is usually compatible with the melodic tendencies of the scale degrees.

Modal music does not (must not!) have strong melodic and harmonic tonal cadences. In fact, such cadences would ruin the modal atmosphere.
Modal melodies and harmonies usually emphasise the mode’s signature.
In modal songs, chords are much less related to the other chords: they “exist” in and by themselves and don’t necessarily “go” anywhere, at least not nearly as strongly as in tonal music.

I hope you found this clear and helpful.