john_tullamarine is right on the money with AFM references.
In the General Aviation world, where a crosswind is considered limiting,
it will be included in the "LIMITATIONS" section of the Aircraft Flight Manual (AFM). Usually Sect 2.
These limits may either be handling considerations or structural limitations.
Good examples come to mind, an Auster J5 had, from memory,
a 10kt xwind LIMIT, it was both structural and a handling consideration.
If you've flown one, you would be indeed brave to venture near the limit unless you like excitement.
Another example of structural limitation is the Piper PA34 Seneca, 12 kts Max Xwind,
any more and you may bend the spar and crease the wing skin as outward proof.
If it's not in the limitations section of the AFM, the manufacturer does not consider it limiting.
As JT has already explained, DEMONSTRATED crosswind is just that, on the day of certification,
it was what the pilot and aircraft demonstrated with the available wind on the day of certification,
and does not imply a limitation.
The Cessna 402C, for example has a "maximum demonstrated xwind velocity of 15kts".
This value is listed in the "Normal Operations" section of the AFM under the heading, "Airspeeds for safe operation".
The Aero Commander 500S (Shrike) has a demonstrated xwind of 25kts.
In the practical sense, if you need to operate beyond the DEMONSTRATED xwind values, you have become a test pilot,
and the insurance company may take an interest in what it was that you were attempting.
From an operational point of view, flight planning an aircraft such as the PA34 with an actual published LIMIT
requires that the forecast crosswind be taken into account at the destination for the determination of the need for an alternate.
That operational "REQUIREMENT" does not apply to a "demonstrated" value,
however the prudent pilot would need to evaluate his personal limits and the owner / operator imposed limits.
So we get down to what you can do legally vs what you should do prudently.
A "LIMIT" has the weight of law, a "demonstrated" suggests you have a good think about what you might be tempted to try.