We have defined it precisely for ease of convention and discussion but its really fuzzy

FAI (International Aeronautical Federation) defines it as 100 km up above mean sea level. NASA and the US Armed Forces use 80 km above sea level.

These are just round convenient numbers to have a threshold. The atmosphere thins steadily as you get higher and higher up so there's no magic line where you're definitely in atmosphere below it and definitely in space above it. The 100 km definition for space comes from an estimate that above that height you'd need to be traveling at orbital velocities to generate enough lift to stay aloft so at that point you're orbiting not flying through the air so its a spacecraft not an airplane.

Aside from a couple test planes like the X-15, most things either operate well under that level (U2 and SR71 could hit about 25km) or well over that level (Low Earth orbit is generally 300-2000km)