Are psi cantrips independent with the same name?

Question

(I know the title is bad, but I couldn't make it good and short, feel free to edit it)

Clark, the 11th level Cleric takes Psychic Dedication as one of his class feats. His Wisdom is 20, his Charisma 16.

He chooses Silent Whisper as Conscious Mind, and Daze as the psi cantrip.

Is the 60 increase to the range valid to Daze globally, or does he actually have two cantrips with the same name:

1. Daze (divine): 60 feet range dealing 2d6+5 damage
2. Daze (occult): 120 feet range dealing 2d6+3 damage

Having two independent cantrips seems logical, as even the traditions are different.

Consider however Brandon the Gnome Bard. He also took the same archetype, but he obviously uses the same Charisma.
If he uses Daze from the Wellspring Gnome heritage to trigger Life-giving Magic, what kind of range will it have?

Answer 1

Psi Cantrips Are Global

Once you've learned a common cantrip as a psi cantrip, all castings of that cantrip are enhanced by your psychic conscious mind.

Psychic Class

Starting with a 1st-level psychic, they learn three standard occult cantrips in their repertoire and three psi cantrips determined by their conscious mind.

At 1st level, you learn three psi cantrips determined by your choice of conscious mind; one is a unique psi cantrip and two are common cantrips, typically from the occult spellcasting tradition, that you always cast as psi cantrips.

Two of the psi cantrips learned are common cantrips that the user always casts as psi cantrips. Without some limitation, "always casting" would apply even when casting from other sources of magic.

Psychic Archetype

The Psychic Archetype doesn't include the full conscious mind, instead having:

You gain a spell repertoire with one standard psi cantrip of your choice from your conscious mind, which you cast as a psi cantrip. You gain the normal benefits and the amp for this psi cantrip, but not any other benefits from the conscious mind.

You definitely cast the spell as a psi cantrip when it's coming from your psychic spell repertoire, but it's less clear that this version would apply more broadly to all sources of spellcasting.

As the ability to always cast the chosen cantrip as a psi cantrip is a benefit from conscious mind, that ability would be included in the "normal benefits" for this psi cantrip from the conscious mind.

Examples

So for Clark, he would be able to cast daze from his psychic spell repertoire or from his cleric prepared cantrips as follows:

1. daze (divine): 120 feet range dealing 2d6+5 damage, Wisdom-based
2. daze (occult): 120 feet range dealing 2d6+3 damage, Charisma-based

Both of these options would qualify to be amped and are considered psi cantrips when cast.

As for myself as a gnome bard, casting daze as an innate spell would still be covered under "always casting" and the spell would be considered a psi cantrip with all the same benefits as above.