You download a large installation image and compare its SHA-256 value with the website. They match. That is useful evidence that your file matches the published value, but it is worth separating integrity from trust in the publisher.
Compare the exact file and algorithm
Use the hash algorithm named by the publisher and the checksum for the exact release and filename you downloaded. A value for another edition or architecture will not validate your file.
If the values differ, stop using that download and investigate the mismatch. A difference does not tell you the cause by itself: you might have the wrong file, an incomplete transfer or a more serious problem.
Authenticate the reference too
If a file and an unsigned checksum are both replaced at the same compromised location, they can agree. A digital signature on a checksum file adds a way to verify it against a signing key, provided you establish that the key belongs to the intended publisher.
Fedora’s verification instructions demonstrate a workflow with signed checksums. Follow the publisher’s current instructions, including how to obtain and check the key, rather than copying commands from an unrelated release.
Keep the conclusion narrow
Successful verification does not prove that software has no defects or is suitable for your computer. It supports a particular claim about the downloaded file. Use it alongside a trusted source, release information and normal installation precautions—not as a blanket certificate of safety.