The first time we see the mention of the 3 or 4 Yogas(I am not entirely sure if Jnana is considered separate from Raja in the Gita) is in the Gita. According to religious tradition, the Gita was spoken by Lord Krishna to Arjuna 5000 years ago. This is based on Puranic timelines which stretch back millions of years ago… However, if we started believing religious history we might as well conclude that the Earth was created 6000 years ago, Adam and Eve were the first humans on Earth, and Jesus was born from immaculate conception.
Obviously one cannot rely on religious history to determine actual history. If we look at secular scholarship on the dating of the Gita, it is clear the Gita appeared much later than the Upanishads and Buddhism. It definitely was not composed 5000 years ago. It is a post-Buddhist text. The Gita has been composed by anonymous author/s and is basically an early attempt to reconcile competing philosophical viewpoints that were in vogue in India then(Samkhya, Vedanta, Buddhism) Hence why the Gita often presents contradictory paths to attempt to include and synthesize as many schools of thoughts that it can. However, it is debatable how successful it is in achieving this goal.
The classical Samkhya school of thought does not support the Samkhya as presented in the Gita. Likewise, the classical Vedanta school of thought does not support the Vedanta as presented in the Gita. Hence, why the need has arisen by many Vedanta scholars to reinterpret the Gita to bring it inline with their doctrine.
Normally, we think of the Neo-Hindu interpretation of the Karma, Bhakti, Jnana and Raja path as being complimentary to one another and leading to the same goal. However, in actuality, these paths are not at all the same and differ from each other markedly. Nor is there consensus that each of these path are equally valid. Many Jnana yogis do not at all agree with the path of Bhakti yogis, myself included. Similarly, many Bhakti yogis do not agree with the path of Jnana yogis. Sankara refuted the Karma Yoga path and demonstrated the superiority of the Jnana Yoga path.
The usage of the terms for the 4 Yogas is also rather ambiguous. Not every tradition interprets them in the same way. The Jnana Yogis see Bhakti as devotion for Brahman which many carry out not through worship of any idol, but remembrance, contemplation and self inquiry i.e. philosophy. The Karma Yogis see bhakti as devotion to their duties. But Bhakti Yogis see bhakti as devotion to an actual personal god, often a very specific god(Krishna, or Shiva, or Durga) and they practice through worshiping idols of their god, chanting the name of their god, hymns to their god and rituals to their god.
The Jnana Yogis see karma as more as mindfully doing whatever duties one has in life. The Bhakti Yogis see karma as simply as service to their god and helping the cause of their god(such as missionary activity to further the name of their god) But the Karma yogi sees karma as dutifully executing every obligation as enjoined on them by their caste and ashrama(age group). There are stories in Hindusim for example how a housewife becomes liberated simply by doing her duties of serving her husband and childern. This is a more liberal and modern interpretation of doing karma yoga, what was traditionally considered to be doing your duties was performing the rituals and rites of the Vedas properly and regularly. This was considered enough for liberation.
Thus every Yoga is a unique and different system to reach salvation. Not all are considered equally valid.
Raja Yoga is an interesting one, because Raja Yoga is not really a Yoga in itself, but rather the science of Yoga itself. It is basically the scientific form of practicing Yoga. It explans why any of the three Yoga’s actually work. How is it possible for example that somebody who worships a god of elephants or a god of monkeys is able to reach enlightenment or attain spiritual powers? Raja Yoga explains: It is not actually the concept of god they are using that is causing their enlightenment, but it is the psychological process taking place in the mind affected by their fervent devotion to a single thought stream, which is allowing the thought activity to slow down and thereby leading to a more purified consciousness and the resultant virtues that come with it.
In other words any kind of practice which can cause the thought activity to reduce will bring about exactly the same effect. There are much more scientific ways of achieving this than worshiping an elephant