What is the difference between Encryption and Signing?

When data being sent to someone is not confidential, but the users want to ensure the authenticity of the data being sent, digital signing is used, as opposed to encryption. Signing is done by feeding the message through a one-way hash, which creates a message digest, and then encrypting the message digest with your private key. The original message and encrypted digest are sent to the recipient, who then decrypts the message digest with your public key, and passes the message through the one-way hash. If the message digests match, then the sender is who they say they are.