An output stage of a operation amplifier or comparator has normally a push-pull output stage to drive an active high or low level on the output. On an open-collector output the high side output transistor is missing. Thus you can only pull the output to a low level and you need an external pull-up resistor, e.g. to +5V. There are comparator with open-collector outputs. An operational amplifier needs an active push-pull output to amplify an input signal. A pull-down resistor(to 0V or negative) is needed if an output has only the high sider driver transistor or on input to avoid floating inputs. You may search for "NPN/PNP/PP outputs" to find examples.
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