To effectively explain the difference between a Coin and a token, I will have to digress a bit and talk about the Blockchain. If you scroll through my feed, you will see that I have been doing a series on Blockchain, what it is, it's features, applications and so much more. So from there we can draw the meaning of Blockchain to be:
A series of interconnected blocks that contain messages cryptographically protected in them. It is a decentralized, digitized ledger that records transaction information about a cryptocurrency in a chronological order. Not only transactions, a Blockchain can be used to record so much more.
Now that we know what a Blockchain is the difference between a coin and a token is relatively easier to explain. A coin has its own Blockchain and is self sufficient. A Coin simply put is a continent that that carry several tokens in it. A coin derives its value from the belief of shareholders that its value will grow and they will make money from it.
A token on the other hand is reliant. It does not have its own Blockchain and it uses the Blockchain of a coin that grants it the permission to do so. The most popular Blockchain used by most token is no doubt the Ethereum Blockchain which houses thousands of tokens. But we also have some Blockchain's like the Tron Blockchain, the Steem Blockchain, and even the Stellar Blockchain.
When using a Blockchain, payment for transactions or gas as it is known is paid in the Coin which owns the Blockchain. For instance, if you want to send BAT from your Trust Wallet or an ERC-20 Wallet to an exchange or something, you have to pay gas in Ether because BAT is an ERC-20 supported token.
So basically in essence, a coin has its own Blockchain which supports many tokens. For instance, the Ethereum Blockchain supports so many coins from BAT, to 1UP, to Parachute, to Dogecoin and many many others. Same way the Steem Blockchain supports many tokens like Steem Dollar, Steemit, Sports Token and others. While a token doesn't have its own Blockchain and is hosted on the Blockchain of a coin.