How would you categorise or distinguish what is a "coin", "cryptocurrency" or "token"?

My thought is:

Coin = unit of measure of a cryptocurrency e.g. BTC where encryption techniques are used to regulate the generation of units of currency and verify the transfer of funds (BLOCKCHAIN)

Cryptocurrency = e.g. Bitcoin, name of the currency in which coins are mined or traded

Token = Service or units of a service that can be purchased, a bit like an API allowance

Is there any benefit to categorising them differently on our website or you consider them all the same thing?

Any thoughts on this would be appreciated.

Many thanks

CoinMarkets