A 4-stroke oil will flow from the crankcase to the engine components to be lubricated and then come back into the crankcase. The oil circulates without being burned.
A 2-stroke oil will lubricate the engine components by association with the fuel (either by mixing with it or by spraying during combustion), so this oil contains components that promote its combustion. Using a 4-stroke oil in a 2-stroke engine can therefore disrupt combustion and cause smoke formation and engine degradation.