The word "Sakyamuni" is correct and usable in written English.
It is most commonly used to refer to Siddhartha Gautama, the founder of Buddhism, who is also known as "Sakyamuni Buddha." The term is derived from his birthplace, the Sakya kingdom, and muni, meaning "sage" or "enlightened one." Example: The teachings of Sakyamuni have influenced millions of people around the world and have led to the establishment of Buddhism as a major world religion.
Sakyamuni is not separate from Amida, and in teaching dharma he manifests the activity or movement towards beings that is Amida's essential quality.
Sakyamuni proceeds to deliver the teaching of Amida Buddha.
In East Asian Pure Land tradition, this royal "tragedy of the capital of Rājagṛha," where Sakyamuni often resided and preached, was understood to indicate that the Pure Land teaching was intended for ordinary, unenlightened beings in anguished circumstances, rather than for a capable spiritual elite.
Further, it is often assumed that while unlettered Pure Land adherents may have clung to the notion of Amida and his vows as real, taking them as objects of faith, more sophisticated Buddhists such as those of the Tendai, Shingon, and Zen schools recognized all along that Amida is merely a skillful "metaphor" or "symbol" for the historical realization of Sakyamuni.
Thus, it is common to view the story of Amida as a narrative fashioned by Sakyamuni (or a later figure) to express the content of his own religious insight.
Regarding the nature of Amida Buddha, perhaps the most natural approach for the modern mind is to focus on the relationship between Amida and Sakyamuni.
In this view, Amida is a fiction whose origins lie in the experience of Sakyamuni.
For Mahayana Buddhists, reality resides not fundamentally with the historical existence of Sakyamuni as such, but rather with that for which he is recognized as buddha, or that which is the motive-force for his appearance in the world, his attainment of buddhahood, and his teaching of dharma.
Sakyamuni, having become the "awakened one" through meditative practices, taught his realization to others, and among the teachings attributed to him is the story of Amida Buddha.
The Seokguram grotto is an eighth-century man-made cave housing a white granite Sakyamuni Buddha, considered one of the most perfect of its kind in the world, one lost to the world until a postman, seeking shelter from a storm, chanced upon the grotto in 1909.
