I don't know how to switch to "false" direct monitoring or "real" direct monitoring for that matter.
What's the difference and how do I get there?
"False" and "real" (or "true") direct monitoring are not official terms. Unfortunately everybody calls it "direct monitoring" or "hardware monitoring" but there are two ways to do it and they are quite different. And no, you cannot switch between them. The two techniques have a different signal flow and major differences in the hardware setup.
There may also be differences between audio interfaces depending on the internal signal flow and wether their "direct" monitoring goes through the analog/digital (A/D) or digital/analog (D/A) conversion or both or none of them. However, below you see examples for two common setups without going too far into details.
Direct monitoring through the audio interface:
You want to hear the recording signal with the shortest possible latency, therefore you do not send the signal through the computer and the DAW but rather through the interface only.
The latency depends on the internal signal flow of the audio interface. Where are the A/D and D/A converters, does the recording signal pass them or not? Do you know your interface good enough? I don't. But the latency is very short anyway, many people are happy with this kind of monitoring and don't care about technical circumstances.
The signal flow is pretty clear, you have to use the internal mixer of the interface. Consult your interface manual to learn how to send the incoming recording signal to the DAW
and to the headphones or monitor speaker(s). Do not send the recording signal back out from the DAW because you would hear it twice: first the direct signal and a little later the signal after it ran through the computer. From the DAW only the playback gets sent to the audio interface.
Direct hardware monitoring:
Hardliners and latency-sensitive people do not insert an interface into their recording signal for monitoring. For this method you split the signal before the interface, either directly after the microphone or after an external preamp. When we agree that analog components (practically) do not produce delay, the latency of this monitoring method is zero.
This is the very best method but splitting weak recording signals is not trivial and requires more equipment. Therefore this "real" direct monitoring is rarely used in home studios.