In addition to the basic function of storing the keys, a crypto wallet may also have one or more of the following characteristics.
Cryptocurrency wallet
A cryptocurrency wallet, comparable to a bank account, contains a pair of public and private cryptographic keys. The keys can be used to track ownership, receive or spend cryptocurrencies. A public key allows for other wallets to make payments to the wallet's address, whereas a private key enables the spending of cryptocurrency from that address. The cryptocurrency itself is not in the wallet. In the case of bitcoin and cryptocurrencies derived from it, the cryptocurrency is decentrally stored and maintained in a publicly available distributed ledger called the blockchain.
eID wallet
Some wallets are specifically designed to be compatible with a framework. The European Union is creating an eIDAS compatible European Self-Sovereign Identity Framework which runs on the European Blockchain Services Infrastructure. The EBSI wallet is designed to provide information, an eID and to sign 'transactions'.
In the cryptocurrency space, smart contracts are digitally signed in the same way a cryptocurrency transaction is signed. The signing keys are held in a crypto wallet.
Key derivation
Deterministic wallet
With a deterministic wallet a single key can be used to generate an entire tree of key pairs. This single key serves as the root of the tree. The generated mnemonic sentence or word seed is simply a more human-readable way of expressing the key used as the root, as it can be algorithmically converted into the root private key. Those words, in that order, will always generate exactly the same root key. A word phrase could consist of 24 words like: begin friend black earth beauty praisepride refuse horror believe relief gospel end destroy champion build better awesome. That single root key is not replacing all other private keys, but rather is being used to generate them. All the addresses still have different private keys, but they can all be restored by that single root key. The private keys to every address it has and will ever give out in the future can be recalculated given the root key. That root key, in turn, can be recalculated by feeding in the word seed. The mnemonic sentence is the backup of the wallet. If a wallet supports the same technique, then the backup can also be restored on another software or hardware wallet. A mnemonic sentence is considered secure. The BIP-39 standard creates a 512-bit seed from any given mnemonic. The set of possible wallets is 2512. Every passphrase leads to a valid wallet. If the wallet was not previously used it will be empty.
Non-deterministic wallet
In a non-deterministic wallet, each key is randomly generated on its own accord, and they are not seeded from a common key. Therefore, any backups of the wallet must store each and every single private key used as an address, as well as a buffer of 100 or so future keys that may have already been given out as addresses but not received payments yet.
Wallet access
When choosing a wallet, the owner must keep in mind who is supposed to have access to the private keys and thus potentially has signing capabilities. In case of cryptocurrency the user needs to trust the provider to keep the cryptocurrency safe. Just like with a bank. Trust was misplaced in the case of the Mt. Gox exchange, which 'lost' most of their clients' bitcoins. Downloading a cryptocurrency wallet from a wallet provider to a computer or phone does not automatically mean that the owner is the only one who has a copy of the private keys. For example, with Coinbase, it is possible to install a wallet on a phone and to also have access to the same wallet through their website. A wallet can also have known or unknown vulnerabilities. A supply chain attack or side-channel attack are ways of a vulnerability introduction. In extreme cases even a computer which is not connected to any network can be hacked. For receiving cryptocurrency, access to the receiving wallet is not needed. The sending party only needs to know the destination address. Anyone can send cryptocurrency to an address. Only the one who has the private key of the corresponding address can use it.
