Since blockchain is a chain of blocks,
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.