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There are several terminologies used to describe Ethereum, a global computer, decentralised AWS, the settlement layer for the internet of value. These terms may sound nice, but they do not aid in our understanding of what Ethereum is, how it functions, or what it ultimately plans to achieve.
This is what the Yellow Paper is for: It outlines in precise language exactly what the Ethereum protocol should do. It exists so that multiple different implementations of the protocol can be created, while limiting the risk of computers that run different implementations falling out of sync with one another. In other words, the Yellow Paper gives the spec of how everyone should stay on the same page.
Implementations of the protocol are typically referred to as Ethereum Clients. The Clients provide the instructions for network participants on how to execute transactions, update the blockchain and verify its correctness. While each computer does not need to run the same client, they do need to run the same logic or they may arrive at a different state, or, version of who owns what assets.
Given the ever-changing nature of Ethereum, there is an ever-increasing chance of errors finding their way into client code. Should two different implementations fall out of sync, the descriptions set forth in the Yellow Paper would be the determinant of which implementation is right and which one is wrong. Thankfully however, the existence of different clients means that even if one falls out of sync, the remaining clients should keep the network running.