The bitcoin code creates a network, which follows a consensus protocol.
The bitcoin code can be forked, and parameters tweaked, in order to create similar, but separate and distinct networks (such as dogecoin, litecoin, etc). Each network will maintain it's own blockchain.
In cryptocurrency, the word 'token' is generally used to describe a special type of non-fungible cryptocurrency asset. It is essentially like a special 'earmarked' piece of cryptocurrency, that can be specifically tracked on the network. A token does not have it's own blockchain, it exists on some parent cryptocurrency blockchain. As an example, the ethereum network hosts many tokens, such as TRX, REP, or BAT. The bitcoin network can also support tokens, through the OMNI protocol.
Tokens follow the protocol rules of their parent chain, but could have additional token-specific rules programmed into them as well.