First analyze the two "zhi"
Zhi means giving; attracting, achieving; mood, situation; meticulous, precise; seeking; dedication; imposing, etc.
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Zhi generally refers to aspirations; marks; notes; recorded words, etc.
Let’s talk about Zhiyuan (Zhiyuan)
Zhiyuan - from Zhuge Liang’s "Jie Zi Pian": "The journey of a husband and a gentleman: quietness to cultivate one's morality, frugality to cultivate virtue. It is not indifferent. To make your ambitions clear, you will not be able to reach far without tranquility. "(Translation: People with moral cultivation carry out self-cultivation and training in this way. They use meditation and reflection to perfect themselves, and they cultivate their noble character through frugality and saving money." If you are greedy, you cannot make your ambitions clear and firm, and if you are not stable and quiet, you cannot realize your lofty ideals and study hard for a long time.) Later generations further extended the meaning of "Zhiyuan" to lofty ideals, career ambitions, and the pursuit of excellence. There is also the artistic conception of "hanging sails directly across the sea". For example, the fastest warship in the Beiyang Navy was named "Zhiyuan", which specifically means riding the wind and waves, being unstoppable and running towards the distance. Therefore, Zhiyuan here means "realizing lofty ideals and achieving career ambitions".
Zhiyuan simply means ambitious, which is the most common meaning.
Through comparison, it can be seen that the former undoubtedly has a better source and is relatively better.