They absolutely are aircraft and governed by the FAA. They call them Unmanned Aerial Vehicles (UAV's). FAA also has jurisdiction over all airspace in the US starting at ground level. There's plenty of reference material on the subject you can read.

When do you differentiate between a toy and a UAV?

The FAA has lighter regulation for drones under 250g, for this reason. But even then, small toy drones of any size are still regulated by the FAA.

Sometimes (often?) technical legal definitions considered without context lead to absurd conclusions that don't manifest in practice.

Does the FAA have jurisdiction over paper planes? What about the airspace in my house and does it matter if the doors are open?

On the other hand, I don't think government agencies have much incentive to preemptively limit the scope of their authority, but would be happy to hear of counter-examples.

This is dangerous and untrue advice. Drones are considered aircraft in the US, and there is no altitude limit or license requirement for something to be considered an aircraft. See 49 U.S. Code § 40102 [0] and explicit FAA regulation of airspace under 400 feet [1]

[0] https://www.law.cornell.edu/uscode/text/49/40102

[1] https://www.faa.gov/uas/getting_started/laanc

This is blatantly incorrect.

See above.

> FAA has no legal authority at low altitudes, except near airports.

False, at least according to this FAA Fact Sheet:

“The FAA has exclusive authority to regulate airspace efficiency for UAS at low altitudes”

https://www.faa.gov/sites/faa.gov/files/uas/public_safety_go...

Me when I lie