In the design of a piston engine running on gasoline, the required octane rating for a particular engine will depend on the compression ratio and the cylinder head temperature (which varies according to how hard the engine is working). High compression ratios and high power settings require high octane fuel to prevent preignition, which damages the engine.
Taking the old-school air-cooled VW flat four as an example, the engine's compression ratio was set at 6:1 so it could run slightly hot on the low-octane (less than ~70) car fuel typical of the late 1930's. This worked out OK because the engine was not continuously run at full power in a passenger car.
Upping the compression ratio to 10:1 or even 11:1 in a car required 100 to 120 octane gas and water cooling, and this was OK again because the car engines did not run continuously at full power. This development occurred after WWII when high-octane gas (originally developed for aircraft engines) hit the car fuel market.
Since airplane engines run at high power setting for long periods of time and have air cooled heads, they will necessarily 1) have relatively low compression ratios (around 6:1), 2) have minimum octane specifications placed by the engine manufacturer on permissible fuels, 3) run rich at takeoff power to scavenge heat, and 4) still have 3-minute time limits on maximum power.