NULL only has one meaning: NULL. This is roughly analogous to unknown.
The one that his a lot of people is WHERE <value> NOT IN (<set>) where <set> contains a NULL. Because NOT IN unrolls to “<value> <> <s1> AND <value> <> <s2> AND … AND <value> <> <sx>” any NULL values in the set makes one predicate NULL which makes the whole expression NULL even if one or more of the other values match.
> I have no way of knowing if that means there's a record [5, NULL] in table y, or if there's no record in table y that starts with 5.
Not directly, but you can infer the difference going by the value of (in your example) y.a - if it is NULL then there was no match, otherwise a NULL for y.b is a NULL from the source not an indication of no match.
> SQL should have specified another NULL-like value
This sort of thing causes problems of its own. Are the unknowns equivalent? Where are they relevant? How do they affect each other? Do you need more to cover other edge cases? I have memories of VB6's four constants of the apocalypse (null, empty, missing, nothing).
This is one of the reasons some purists argue against NULL existing in SQL at all, rather than needing a family of NULL-a-likes.