i think i might be able to add a bit of context here to help out.
We begin with yoga as one of india's classical philosophies--one of six: Nyaya, Visheshika, Mimasa, Sankhya, Yoga, and Vedanta.
In the broadest context, there are two 'types' of yoga--Raja Yoga and Tantra (or Kundalini) Yoga. This refers to two primary perspectives of achieving yoga--or methods you could say. Raja Yoga means "royal yoga" and tantra or kundalini yoga refers to the divine feminine which is manifest in origin and and arising, liberating process from the manifest origin.
in many ways, raja is the brahmic path--which is an appollonian path. This sort of path is tipified by ideas of 'transcending flesh' or manifest aspects. tantra yoga is it's opposite--a dionyesian path--tipified by ideas of integrating all aspects of being to develop enlightenment.
Both types of yoga utilize--in various ways--the four sub-types of yogas or yoga paths: karma yoga, bhakti yoga, hatha yoga, and Jnana yoga. karma yoga is the yoga of service; bhakti yoga is the yoga of devotion; hatha yoga is the yoga of postures and pranayama; and jnana yoga is the yoga of knowledge from scriptural study, discussion, and contemplation. Now, sometimes, Raja is substituted for 'hatha' here, because raja includes hatha and also refers to the meditative practices of yoga philosophies. It could be called "the yoga of meditation." but, because raja transcends the various methodologies--and includes them--and jnana, bhakti, hatha, and karma all include the meditative aspect that is referential to raja, i use raja as the overarching term or type based on focus or work of that type as opposed to the tantric perspective--even though both reach the same result, which is Yoga.
hatha yoga, therefore, encompasses and/or includes any form of yoga that utilizes postures and/or pranayama. thus, bikram, kripalu, sivananda, power yoga, whatever uses a pose is hatha yoga.
under hatha yoga, there are roughly two alignment schools in the modern era: Krishnamycharya and Bihar. The krishnamycharya lineage has one type of alignment taught by krishnamycharya to his students such as Iyengar, Pattabhi Jois (astanga--based on Patanjali's Yoga Sutras where he refers to it as Raja yoga, which is why sometimes raja and hatha are interchanged), and Desikachar. the bihar school is the sivananda school.
unless i'm mistaken, bikram was taught by gnosh, who was taught in a way that is similar to the sivananda style. If sivananda and gnosh didn't learn from each other, they likely learned from a similar teacher or lineage. so bikram's yoga is of a different lineage than other forms.
for the most part, every 'style' of yoga in the west is rooted in one of these two schools of alignment (how postures are done and why). The differencs are largely in how the information is presented. for example, in my experience with kripalu, it seems to function with both alignment schools, because it simply takes a different philosophical perspective of how to approach postures, without any overt expression about which alignment is "right" (bihar vs krishnamycharya), but that the perspective can be used for both. so a kripalu class can have either form of alignment, but a different perspective of how to approach that.
bikram yoga's alignment is like sivananda's lineage, but obviously bikram has his own take and his own reasons for that take. there's nothing inherently magical about his 'take' over others, but it does work toward the goals that birkam puts forth for his series. he asserts that his series will lead to these physical results, and they often do. other teachers--from whatever lineage--assert the same things.
but for all, the goal is the same. the goal is yoga. Yoga is a spiritual practice/experience with a physical component. But we often begin with the physical component because it is most obvious, the most accessable, and if the body is healed, then it can be transcended (whether transcended in the raja sense or transcended with inclusion in the tantric sense) and we can work at that 'next level' in the mind, and then transcend to the next level, and next level, until we reach that point called Yoga.
So, hot? sure.