The simplest way to think about it, maybe not the correct way, but the simplest is that "Western" and "Eastern" philosophy are different gardens. "Western" philosophy is often referred to as the "Confluence of Jerusalem and Athens" referring to the basis of Western Philosophy being the Logical schools of Socratic Philosophy and Judeo-Christianity.

There really isn't an "Eastern Philosophy" by contrast. Comparatively, we do have large fields of Chinese and Indian philosophy, usually collectively referred to as "Dharmic," though it'd be a false dichotomy to compare it with Western Philosophy as a kind of "Confluence of China and India."

"Dharma" in Sanskrit literally means "Law," as in "the law of nature." When "Dharma" is referred to in Indian texts, it often refers to religion as a whole, but it's original meaning was in reference to the functioning of the universe. Indian philosophy, the Dharmic Philosophies we can largely* group together under the banners of Hinduism, Buddhism, and Jainism, is rooted in the Vedas. Hinduism grew out of adherence to the Vedas, Buddhism and Jainism as a rejection of Vedic authority. Both, however, still rely on the concepts of Dharma and all three share ideas about the cycles of rebirth and the cyclical nature of time and the universal creation and destruction. Buddhism (I cannot speak for Jainism) began its life as primarily oral and soon developed a tradition of texts much like its developing older sibling Hinduism, which spent much of its history relying on a few (albeit long) texts. As the three developed, Vedic religion into Hinduism and its many (many) schools, Jainism's two, and Buddhism's many (that can be grouped into three main groups: Theravada, Mahayana, and Vajrayana) so did scriptural and textural traditions.

Chinese philosophy can trace most of its roots from the Yijing, the Book of Changes. Kong Tzu (Confucius) and his followers famously studied it, Taoism is strongly rooted in it, and Buddhists were keen to adopt it into their own understanding and corpus. Even the Jesuit missionaries, when they saw the possibility of adding an empire's worth of souls into the Catholic Church, saw fit to understand and adopt the Yijing into their worldview. The Book is many things, but is most famously a divination text used to guide rulers and governors towards paths of righteous behavior and living, even if (especially if) decisions are difficult. Richard J. Smith writes that Chinese culture "is" the Yijing. Examination of the text's numerology points to a connection with Shang and Zhou Dynasty Bone Oracles, in which questions were inscribed on the carapaces of turtles and then burned in a way to produce cracks in the shell, which were then interpreted by diviners. These numbers correspond roughly to the imagery of the Yijing's gua**.

Without getting lost in the weeds, this was the earliest record of Chinese thought (and pretty early in general for the timeline of human writing) though the Shang and Zhou Dynasties did pretty well to annihilate turtles in China and so reliance on the Yijing and its interpretation grew. By the period of the Warring States, it was one of the few books that was universally regarded and one of the primary one that scholars took great lengths to study. See again, Kong Tsu's well known adherence and understanding of the Yijing.

To sum up, if we have three gardens of work, the initial seeds of Western Philosophy were Socrates and the Hebrew Prophets. The seeds of Indian Philosophy were the Vedas, which produced new varieties as well as reactions to their interpretation. The garden of Chinese philosophy was initially seeded by the Yijing which sprouted new varieties and interpretations. As the gardens grew and new plants grew, either as reactions to what was already there, or as offshoots and cousins of what came before them, trade routes became more developed and pronounced and the gardens began to experience cross-polinization. The Silk Road was first established between China and India and almost immediately Buddhism began to seep into Chinese thought. At first, a philosophy that shunned families and admired the cloistered ascetic, that was based in rebirth and couldn't comprehend the idea of an ancestral heaven was shocking and offensive to the Chinese, and remained solely an academic exercise. But slowly, it began to infiltrate and now the many East Asian schools of Buddhism are rooted in the Chinese Canon, translations of the Sanskrit originals. Meanwhile, similar processes have happened/are happening with the introduction of Western Philosophy to India and China, though we're quickly zooming out of my area of expertise.

Note that this doesn't touch at all upon Islamic Philosophy, or Southeast Asian Philosophy, to say nothing of the varies smaller gardens of native philosophies around the world. I'm a Tibetologist who's interested in Silk Road topics and deal frequently with the exchange of ideas across Asia.

*largely. This is a basic overview.

**In English we usually use the term "hexagram" and "trigram" for images of six lines and three lines, respectively. AFAIK, Chinese does not distinguish between them.

Sources:

India: A History, and China: A History, by John Keay

A Concise History of Buddhism by Andrew Skilton

Fathoming the Cosmos and Ordering the World and The Yijing: A Biography by Richard J. Smith