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Since blockchain is a chain of blocks,

In ethereum,

1. is there only one chain of blocks 

2. are there multiple chains of blocks.
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In Ethereum, there is one chain of blocks which is network id: 1, the "mainnet".

Of course, anyone can use the software to produce any number of non-official blockchains. Public "testnets" are commonly used to debut/preview new systems for testing and review purposes. More on these here: Comparison of the different TestNets

Private networks consist of a handful of vetted nodes. For example, a developer can set up a small network with as few as one node. An enterprise or consortium can set up a small network of vetted nodes.

Both testnets and private/consortium networks have different blockchains and states.

We might say "Ethereum" has only one blockchain, but there are unlimited instances of "Ethereum-like" blockchains using the same underlying software but different blockchains. Block explorers show how they are separate universes.

Hope it helps.

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