When I speak about phrygian cadence in tonal context this is generally the minor half-cadence. Yes, it is a confusing habit from tradition. This confusion might have started with Schoenberg, see the example below . If you teach by his book one time you start just calling it Phrygian Cadence and forget the “to V”. Even though, strictly this means: the V is a iii now?!
Actually – since most of the time there is no need to bring the concept of phrygian cadence in tonal context unless we talk about these situations:
– the authentic Phrygian cadence on phrygian finalis
– there is some important reference to old modal voice-leading praxis, and this is mostly the case with IV and IV6, or VI, exactly the chords of hals cadence…and source of confusion .
– a modal interchange in a conclusive cadence that is not to be mistaken by a half-cadence, for example in some cases where the neapolitan preceeds the tonic in the last chords of a great epic soundtrack scored by Miklos Rosza, after he drinked some extra bottles of wine 🍷, and what I call post-cadencial intensification (piece ended on tonic, but the composer keeps composing more over the pedal point …) I have some examples collected on this topic, because it is one of the keys to extend cadences beyond the narrow universe of “prinner… fonte…cadenza doppia/cadenza cappuccina et machiatta…”The best i hold for later…
In context of modern (pan)modal harmony you might want to use this epxression always when there is an ending with conclusive nature that uses the half-step relationship typical of a phrygian cadence. In this case it makes sense to use the expression and the context makes clear that the mode is not authentic, but transposed. What else? Wanna call it Le Negative COllier?
The ONLY problem is the contradition between the conclusive nature of the authentic phrygian cadence and the open nature of the minor half-cadence. The first has a pichard third adding consonance to the minor triad on the finalis, the second has a raised third working as tensioon: it is the LEADING tone of a triad on V scale degree. This contradiction creates problems representing the most important aspect of an ending: if it is felt as open or conclusive.
We have still here a wide spectrum of possibilities: a tense conclusion in one hand (authentic phrygian,) and a relaxed opening in other hand: the minor half-cadence with the phrygian leading tone above, and the tenor clause ascending from below (from subdominant, principally when the 4/6 chord is used as apppogiatura on the dominant, before its resolution in the root position ).