Question: As the Buddhas can manifest in many forms, about Śākyamuni Buddha (释迦牟尼佛) and Amitābha Buddha (阿弥陀佛), could one be a manifestation of the other?
Answer: There are 3 ways to understand their relationship, in terms of Sequence, being Siblings and being the ‘Same’.
 Sequence: First, as Śākyamuni Buddha is our fundamental teacher (本师), who introduced us to Amitābha Buddha as a transhistorical Buddha (who transcends our current human history), it is best not to conflate or mix up the two. In this sense, according to the Amitābha Sūtra《阿弥陀经》, we usually see Amitābha Buddha to had attained Buddhahood 10 kalpas before Śākyamuni Buddha, which is why the latter could speak of him as an earlier Buddha.
 Siblings: Second, as Śākyamuni Buddha taught in the Wonderful Dharma Lotus Flower Sūtra’s《妙法莲华经》7th Chapter On The Manifested City’s Parable (化城喻品第七), Great Supernormal Wisdom Supreme (Mahābhijñājñānābhibhū) Buddha (大通智胜佛) in immeasurable kalpas ago, had 16 princes (i.e. sons) when he was still a king, who later became his Bodhisattva Śrāmaṇera (菩萨沙弥) disciples, whom he predicted will attain Buddhahood. The 9th son was predicted to be named Amitā[bha] Buddha, and the 16th son as Śākyamuni Buddha. In this sense, they were older and younger brother princes respectively in a distant past life.
 ‘Same’: Third, we say that all Buddhas are combined as one in terms the Dharmakāya (法身) as a universal and boundless body. In this sense, every subsequent Buddha is a manifestation of all previous Buddhas too. As each Buddha can manifest walking the path to Buddhahood innumerable times, it is difficult to say which of the two Buddhas first arose as a Buddha. However, in the spirit of the universal Dharma realised and taught, the latter Buddha could be said to be a co-manifestation of the earlier Buddha.
To summarise the above perspectives, scripturally speaking, before attaining Buddhahood, the two Buddhas-to-be were two persons distinctly, although related conventionally. However, after both have attained Buddhahood, in the context of the Dharmakāya, they can be said to be ‘one’ ultimately, although usually still taught as distinct to avoid confusion. They also function ‘separately’ yet ‘similarly’, as recorded in the scriptures.
Śākyamuni Buddha’s Pure Land On Spirit Vulture Mountain (And Related Pure Land Concepts)
Please be mindful of your speech, Amituofo!