It is recommended to supply a voltage to the input pin so that the logic of the output is fixed. When determining output logic High or Low, set it arbitrarily on the assumption it may be shorted with the output peripheral circuit.
Operation outside of the common mode input voltage range is outside of the guaranteed electrical characteristics. In the case of an open collector comparator, as long as the supplied voltage at one of the input pins is within the common mode input range the comparator will operate normally. However, when the voltage supplied to both input terminals falls out of the common mode input range the output will be fixed at Low. But with the BA10393/BA10339, if an input voltage higher than the supply voltage is input there is a possibility of destruction due to breakdown voltage.Related Link：Technical Document
Please verify the graph of the Input Offset Voltage vs Common Mode Input Voltage Characteristics included in the datasheet. The point at which the input offset voltage suddenly changes becomes the actual value for the common mode input voltage range.
There is no problem with the conventional method. Shorting the + and -input pins and connecting them to VEE. In this case the input offset voltage is multiplied by the open loop gain and the output is fixed to High or Low. In the current datasheet the -input terminal is connected to VEE and the +input connected to a potential within the common mode input voltage range higher than VEE. This allows the output to be fixed and supports high impedance, making it recommended for all comparators. Connecting the +input pin to VCC will place it outside the common mode input range, but this shouldn't be a problem.
-C and -M are not differentiated by temperature but by application. -C is designed for sets involved in vehicle travel control systems (running/turning/stopping) and advanced driver support systems while -M products are intended for car audio/navigation, door locks, AC, display, and communications systems.