In practice, public key systems are clumsy to use in transmitting long messages. Instead they are often used for Key-Exchange of Symmetric Keys, which are relatively short. The Symmetric Key is then used for the Data Encapsulation Method the longer message.
The traditional approach to sending a symmetric key with public key systems is to first generate a random symmetric key and then encrypt it using the chosen public key algorithm. The recipient then decrypts the public key message to recover the symmetric key. As the symmetric key is generally short, padding is required for full security and proofs of security for padding schemes are often less than complete. KEMs simplify the process by generating a random element in the finite group underlying the public key system and deriving the symmetric key by hashing that element, eliminating the need for padding.