I'm not sure there's an "official" definition, but generally crypto(currencies) are referring to currencies that are setup on a blockchain, or distributed ledger. In addition validator models, such as proof-of-stake and proof-of-work are used to validate and maintain the ledger.

A digital currency does not require a distributed ledger, nor does it require a validator model as it is not distributed or trustless to begin with as it's inherently centralized and backed by a government and existing monetary infrastructure usually.

In other words, digital money is nothing like cryptocurrencies.

I agree there is a difference but nothing about a cryptocurrency or blockchain requires a distributed ledger or distributed consensus mechanism. In fact there are plenty of centralized cryptocurrencies out there today.

Entries in a company’s database do not a cryptocurrency make.

Maybe if they used an authenticated append-only list to store the state or state changes, and published a summary of the head periodically in a way such that users could at least validate that the state changes were valid, or at least not violate certain rules, that might count.

If cryptography isn’t used in order to make something verifiable, it isn’t really a cryptocurrency, I’d say.

A blockchain is a database of blocks which are cryptographically hashed such that manipulating any previous entries would invalidate all future ones referencing it. That is pretty much it. This can be constructed on a single machine in someone's basement if one so desires. In fact, the entire point of Bitcoin is that the entire blockchain can be validated by any node which anyone can start with something as trivial as a raspberry pi. Now Bitcoin adds a decentralized mechanism on top of this using Proof of Work. But that is not inherent to blockchains.

Yes, I think that fits under (or is perhaps synonymous with?) the “authenticated append only list” that I said.

I think the term referrer to cryptography aspect of the currency.

In a blockchain system, you can generate transaction off-chain(as in, no need for internet access), then you signed it with your private key, and send to a node in the chain. The nodes can verifiy/confim using your public key. The wallet address is a result of hashing your public key.

Compare with a digital currency, you most likely need an account and some sort of credential that managed by the company which issues the currency.

Cryptocurrency is a distributed ledger over a blockchain. The real question is what is a digital money ?

Digital money is the digital equivalent to cash. It's money that is emitted by the central bank in digital form that you really own, not a debt that a bank somehow owes you.

Cryptocurrency or not, central bank application or other, it's all implementation detail. The important definition is : it's money you can own but that you can't touch.