Since blockchain is a chain of blocks,
In ethereum,
1. is there only one chain of blocks
2. are there multiple chains of blocks.
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.