Ha = sun, Tha = moon. The sun and moon are believed to be the opposite currents that regulate bodily processes. Hatha Yoga mainly focuses on Asanas (postures) to balance the energy current in the nadis (energy channels like arteries, veins, etc). It includes Asanas, Shat Karmas, Pranayama, etc. Nowadays, when people usually say ‘Yoga’, they mean Hatha Yoga, that too only of its physical practise of Asanas.
Raja Yoga or Ashtanga Yoga
Raja = king. Raja Yoga is the Royal Yoga, the supreme form of Hatha Yoga, its crown, its master.
Ashta = eight, Anga = limb or part. Raja Yoga is called so, because of the eight limbs it has.
It deals with 'higher levels of perfection', like improving the already increased concentration originally increased through Hatha. Like Hatha Yoga, it also includes asanas. It mainly focuses on purification of the mind.
Bhakti Yoga
Bhakti = devotion. This is about the positive traits (feelings, here) like love, purity, desire, devotion to God, etc. It need not be connected with the Yogic asanas we see in pictures. It is ‘namaskara’ or ‘namaaz’ or ‘salutation’ or ‘devoid of ego’ or ‘prayer’, but it usually involves adherence to religion or faith. Only the Almighty God can value the Bhakti Yoga of a person. According to religions, it is primarily the Bhakti (devotion) that God uses as a scale to decide whether to allow one to enter Heaven, besides other actions and deeds.
Jnana Yoga
Jnana = knowledge. Jnana Yoga is strictly about philosophy. Jnana Yogi uses his intellect to study the metaphysics of one's own self. It finds who he is and what he is, by thinking. It is about an introspection of the Yogi. It helps us find answer to problems of life. Jnana Yogi achieves self realization through knowledge acquired through his own application of mind over matter with utmost intelligence.
Kriya Yoga
Kriya = action or deed. Kriya is the verbal component of life. Kriya Yoga aims to release the body and mind of difficulties, obstacles and obstructions. It necessarily relates to the Kriya we do for ourselves. It calms the mind and body through meditation and chants. It controls the cosmic energy (life-force) or the Kundalini Shakti of the person to unite the mind, body and spirit.
Karma Yoga
Karma = action or deed. It includes everything we do for others' good. It is dharma. It relates to our actions for others. It is important to note that we should 'act' without negative traits like selfishness and hatred. Karma Yogi acts because he loves to, not because he has to. This is the essence of a Yogi. Karma Yoga aims in the purification of us by serving our fellow beings, by serving the other servants of Almighty God, thereby pleasing the God.
Tantra Yoga
Tantra = principle or doctrine. Tantra is a different way of life, and contributed to the Yogic discipline of life, and later found to have strong similarities, and subtle differences in mystical metaphysics. The practice of Tantric meditation should be done with extreme care under a right ‘Guru’.
Kundalini Yoga
Kundalini = coiled. Kundalini is a force that lies coiled in the base of the spine. It is also pictured as a sleeping snake and hence it is a.k.a. ‘serpent power’. Kundalini Yoga is specifically to awaken the Kundalini Force and certain Yogic Asanas are remarkable for this with years of practice. It is an expanded sensory awareness and spiritual consciousness, and people might feel energy or electric-like circulation in the body. It has its roots in Tantra Yoga.