Peril is not in the cultural difference. Peril is in wanting to see complex things simplified like an equation. For example, when Einstein’s elaborate mathematical model is reduced to e=mc2, it appears suddenly ‘yours and mine’. Peril is also in our bringing down multi-dimensional phenomena into a single dimension that our lmited perceptibility can take.
None of the three equations is fully correct. If, this whole perceived universe and each object belonging to it is an interplay of the Spirit and the Matter(Purusha and Prakriti), the Spirit is present in everything. Thus, Spirit is ‘present’ in both prana and kundalini, but not equal to either.
Prana is Cosmic Energy. At the highest dimension it exists in an absolute form in the most subtle state where it is also Universal Mind. While Cosmic Energy degenerates into 5 different vayus inside any object, Universal Mind gives birth to more & more gross matter and gets entangled and hence morphed as individual mind. So, what is One in the highest dimension, becomes many and degenerated in the lower dimensions.
However, things at the lower level have a potential to be pure and potent again, given the circumstances. Kundalini is this potential pure energy that remains unmanifest and inactive at muladhara chakra. This chakra is designed to generate energy by fusion since birth and carry that energy through sushumna nadi to activate and sustain rest of the chakras up the spinal column. When the spiritual practices make this possible, kundalini is manifest and active energy. Parallel to it, spiritual purification process makes vayus as pure as prana and they combine and rise up in the body helping kundalini’s ascent.
So, in my view, prana and kundalini, in their purest form are the same, at the highest level and ultimately when anything is separated from matter it is the Spirit. But in the lower/ gross dimensions and through most of our spiritual journey, the three remain distinct. I would love to learn how this is seen in other streams of thought.