Yoga, in sanskrit, means union; the sun and the moon, the internal and the external, the past and the future. The goal of yoga is integration of the self through self-discovery.
“Classical” yoga practice is several thousands of years old. The Raja Yoga (Royal or Kingly) is an eight-fold practice and Hatha Yoga is one of those branches. In this context hatha yoga is the physical practice including asanas (postures) and pranayama (breathing exercises).
The classical style is to practice the sun-salute and twelve specific asanas in a specific sequence to calm, focus, and energize the whole body. This is done especially to support another branch of Raja Yoga, meditation. If the body is uncomfortable or asleep then meditation cannot be accomplished. When the the body is comfortable but alert then you can meditate. With hatha yoga the body is aligned and tuned.

Every other kind of yoga is a derivative from the classical hatha yoga. People take out things that they don’t like and add things they imagine are better – or these days they add things that they think will sell places in the room. Popular yoga these days often includes features people imagined or collected. You may benefit from such a yoga class but the core principles of mental focus and physical atunement can be quite diluted in a yoga class in a gym with props and no breathing exercises and no sanskrit chanting.

Classical style hatha yoga relies on no ‘props’ besides a simple mat. The props you see for yoga are modern accessories. They are often useful from a Phys Ed point of view but they contribute nothing to accomplishing the core goals of yoga.

In Vedic Sanskrit, yoga (from the root yuj) means “to add”, “to join”, “to unite”, or “to attach” in its most common literal sense. Compare the figurative uses of “to harness” as in “to put something to some use.

The Sanskrit-English Dictionary definition of hatha is “violence, force; obstinacy, pertinacity”. On the face of things then, hatha yoga is the “forceful yoga,” a reference to the vigorous methods – like posture (asana), conscious breathing (pranayama), and various body “seals” (mudra) or muscular contractions, that yogis of this school employ to storm the gates of self-liberation.

Now what does hatha’s esoteric definition of “sun-moon” mean? There are several differing interpretations, but they’re all based on the teaching that every living creature is powered by a subtle energy called prana. The Prana breathing element is the hallmark and centerpiece of Hatha yoga and what distinguishes it from most other forms of yoga, like Flow Yoga or Bikram (hot) Yoga.

There are many sub forms of each style of Yoga and one in particular which is the style I practice is Iyengar Yoga. Iyengar, is a form of Hatha Yoga that has an emphasis on detail, precision and alignment in the performance of posture (asana) and breath control (pranayama). The development of strength, mobility and stability is gained through the asanas. What makes Iyengar to me so great is it takes all the great qualities of Hatha and takes it deeper with the use of props. ie blocks, straps, chairs, bolsters. The use of props allows those that are not so flexible or strong, that may have physical limitations, disease or injuries to do the Asanas (poses) with modifications and support that allow the student to do a pose with less strain and this allows the student to better relax and do the most important aspect of Hatha Yoga and that is the Prana (breathing) part of the pose.

Yoga’s true purpose is to balance the body physically and to prepare the practitioner for meditation and Hatha Yoga does this the best.

It is more related to body than mind. Body postures are difficult compared to normal Yoga which is based on breath control. Each Yoga has its plus points so not sure we can say one is better than other.

It is a special type of yoga to enhance skin, muscles, and bones. It is costly because it is done under some professionally knowledgeable trainers.