It's somewhat common to limit password lengths to avoid DoS attacks that exploit a slow key generation function.

But that limitation should on some hundreds or a few thousands characters. Sites that use limits like "16" are probably storing them as plain text.

I appreciate your comment anyway! I didn't know passwords would be hashed to a consistent length - I can see how that would be more secure.

I don't think in the cases that I mentioned, that the hash of my entered/saved/extralong password was being compared to the stored hash they had on file, I think what happened is the input field validation was changed and would no longer allow a password that was valid under their previous rules.