The terms cryptocurrency, token and asset are not mutually exclusive.
However, there are specific definitions that show a subtle difference between these three terms:
Cryptocurrency is a digital asset that circulates on the internet as a medium of exchange. It employs blockchain technology — a distributed ledger of transactions that is publicly available — and is secured by advanced cryptography. This revolutionary asset architecture allows for certainty that cryptocurrency coins and tokens cannot be double-spent even in the absence of a centralized intermediary. The first cryptocurrency to achieve mainstream success was Bitcoin which paved the way for the proliferation of many other cryptocurrencies.
Within the context of blockchain technology, a token generally refers to a unit of value for a programmable asset that is managed by a smart contract and an underlying distributed ledger. Tokens are the primary means of transferring and storing value on a blockchain network [...]. Tokens can also be designed to be either fungible or non-fungible, depending on a network's specific needs. And while many tokens are primarily used for simple transactions, an increasing number of blockchain projects are designing tokens encoded with a variety of wide-ranging use cases, primarily in regards to on-chain governance and network maintenance.
An asset is anything of monetary value that can be owned or purchased. Within the context of investing, assets can refer to a variety of financial and physical instruments, from stocks to real estate to gold to dollars. A bitcoin is a particular form of crypto or digital asset.