Krisha Mitra Das —
I like to start off by saying the Yoga path is a philosophy...
Yes, I think that's a safer path in the West.
Of course there are two sides to every coin — Buddhism, it is often said, is a philosophy, not a religion, which is bunkum really, as Buddhism ticks all the boxes of a religion (if not confined to a particularly narrow, monotheist sense), and all religions contain, in more or less explicit manner, a philosophy.
The distinctions between 'religion' and 'philosophy' are largely a western, post-Enlightenment classification, and ever since it's become fashionable to declare that the philosopher isn't constrained by religious superstition, and the religious isn't troubled by thinking for him/herself!
Yoga means union in Sanskrit, specifically a path of deeper union with the Divine/God.
Yoga has been popularized as just poses, stretches or exercises ...
Consumerism does this: it looks to see how it can monetise everything that falls within its gaze. So it's tough to sell traditional yoga, it's a lot easier to sell keep fit. Same with meditation. Now it's almost as if mindfulness is the be-all and end-all of meditation practice.
The yogas you mention are, of course, universal, and are there to a greater or lesser degree in all religions.
Speaking as a Christian, I think it's a pity that 'the body' has accrued such negative connotations. We've lost so much via this process, and you have to look quite hard to find the equivalence, usually locked away in monastic practice.