What is a cryptographic checksum and does it verify files?

How to Verify Checksum on Linux

Suppose that one byte in a buffer covered by the Internet checksum algorithm needs to be decremented (e.g., a header hop count field). Give an algorithm to compute the revised checksum without rescanning the entire buffer. Your algorithm should consider whether the byte in question is low order or high order. | Numerade

What Is the Checksum on a Credit Card? | Sapling

Checksum: The Simplest to Calculate the Checksum for MD5 and SHA256

Checksum - File Integrity Check on Linux Command Line - Putorius