Historically, a coin has always been a piece of metal that was used to represent a certain value. But all that's changed with the advent of digital currencies.
The modern definition of a coin is somewhat different from what it used to be because now we are also talking about cryptocurrencies. Every cryptocurrency is independent of every other cryptocurrency, and a coin can be defined as the token associated with each one of those platforms, but it can also be used to describe a crypto asset that isn't a token.
Unlike crypto tokens, coins aren't meant to perform utilitarian functions, such as representing votes in a community or denoting storage capacity on a cloud service. Rather, a coin works within its own specific blockchain and each service uses its native currency for its own financial system. So, a coin enables the storage and exchange of value within the realms of its own digital economic network.
The majority of blockchains function as decentralized, distributed ledgers that track and verify every transaction, and their coins only work within their own ecosystem.
Unlike a physical coin, a digital coin does not have a face value, but in a similar way to a fiat coin, it can be exchanged with someone else at whatever rate the market says it is currently worth. It can also be exchanged for fiat currencies or other cryptocurrencies on different blockchains using a cryptocurrency exchange as an intermediary, or via private transfer methods (such as peer-to-peer and OTC trades). Decentralized exchanges and so-called atomic swaps are also ways of facilitating token and coin trading.
Many new blockchain companies use a crowd sale method called an Initial Coin Offering (ICO) to raise funds for their new venture. Most of these have used the Ethereum network, issuing tokens using the Ethereum Token Standard protocol (ERC20). The advantage of this is that they can use an existing blockchain network to raise those essential early funds instead of using their native coin.
Typically, start-ups will accept Bitcoin or Ethereum in exchange for these ICO tokens, but some are happy to accept fiat currencies or even other cryptocurrencies to aid their fundraising efforts too. Sometimes the ICO coin will have some kind of link to the intended coin and can be eventually exchanged for it when its blockchain is up and running.