A paper wallet is a collection of seed phrases written on paper. A seed phrase is some number of words (typically 12 or 24) that can be used to regenerate a keypair on demand.
In terms of convenience versus security, a paper wallet sits at the opposite side of the spectrum from an FS wallet. It is terribly inconvenient to use, but offers excellent security. That high security is further amplified when paper wallets are used in conjunction with offline signing.
A hardware wallet is a small handheld device that stores keypairs and provides some interface for signing transactions.
A hardware wallet, such as the Ledger hardware wallet, offers a great blend of security and convenience for cryptocurrencies. It effectively automates the process of offline signing while retaining nearly all the convenience of a file system wallet.