A cryptocurrency wallet is a secure digital wallet used to store, send, and receive digital currency like Bitcoin. Most coins have an official wallet or a few officially recommended third party wallets. In order to use any cryptocurrency you will need to use a cryptocurrency wallet.
Here is a link to Compare all top cryptocurrency wallets in one place,
What is a paper Wallet
A bitcoin paper wallet is just the Bitcoin private key printed on a piece of paper. A paper Wallet is one particular medium of holding the private key. Paper wallets are a form of cold wallet and essentially a bearer instrument – whoever holds them has access to both the Bitcoin private key and therefore the address.
What is a Hard Wallet
A Bitcoin Hardware wallet is another form of cold storage just like a paper wallet as the Bitcoins are stored offline. They have most of the security of paper wallets in that they are only vulnerable to physical theft but remove the process of having to load the private key in wallet import format to some software which is exposed to online vulnerabilities.
Hardware wallets are in two parts – one connected device and one disconnected.
What is a private Key
A private key is just a number picked at random. The private key is used to generate the public key through an irreversible process. In the case of Bitcoin the Private key is turned into the Public key through Elliptic Curve Cryptography or ECC for short.
If you lose your private key you can't access your Bitcoins, and if someone else finds it out they can steal them.