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As far as I understand Message Digest is a certain Hash function that is derived from the original payload, so that even if a single bit changes the Message Digest proves to be different, thus indicating a failure of data integrity. When it comes to Checksum, I know that it is used for error detection, and is based on a similar mechanism.
What is the difference? Why name two different things?
A checksum is the general term used. A checksum can range from a check digit (parity bit) to a complex output string. Different checksums (examples below) can be chosen depending on the application.
