Tantra yoga is not a path, and it does not focus on sex (that is a western misconception); it is a subset of yoga or style that raises the consciousness by opening creativity. There are four paths of yoga, Jhana (which actually means to obtain true wisdom of self, and that is why it's hard to master), Karma (yoga of selfless service), Bhakti (devotional), and Raja (as written down by Patanjali). Hatha Yoga is a branch of Raja, developed in the 14th or 15th century when the yoga pradipika was written by Swami Swatarama. Hatha yoga is not solely about asanas; it includes pranyama, mudras, mantras, etc. so that the practitioner can attain samadhi (conscious awakening) by awakening the kundalini (subtle engergy). So, Hatha yoga is a whole system; it just not taught that way in a lot of places in the U.S. About Kundalini: There is the term "kundalini", and there is Kundalini yoga. The term,"kundalini" is the subtle energy that runs (generally speaking) along the spine; many forms of yoga can be practiced to awaken the kundalini for self-realization. Kundalini yoga is a style of yoga or sub-set from the Raja path and Hatha yoga branch. Kundalini yoga classes usually have kriyas (yoga poses, breath, mantras, mudras) done in specific ways to safely awaken the true nature of self or self-realization. Kundalini yoga is beautiful, but it's important to only go to a properly trained (certified) Kundalini instructor. Teachers of other traditions should not be teaching kundalini yoga (some teachers add bits and pieces of kundalini yoga to their classes - this is not good). No, I am not a kundalini teacher; I am certified in another style, but I am a kundalini student.............. Also, it's not "Self-consciousness...that is something else.... Namaste..........
Hatha Yoga originally is not a branch itself but it was a part of Raja Yoga. Modern day yogis (including me) making it seem like it is the "very yoga". But nobody in the history of the world has attained Self-consciousness or the real "union" just by practising asanas, as far as I know. So it is not a whole system or branch.
I did not see an explanantion of Hatha Yoga among these.