Why are the resistors all different?
4.7K is sort of a "strong" pull-up resistor, usually I see 10K to VCC (in your example, 3.3V) 

The 100K is a weak "pull down" which avoids a floating pin during system reset or other odd occasions. This is common when you want deterministic start-up conditions on driven inputs/outputs - usually during power-up, or reset, as I mentioned. 

Pull up resistors that I mentioned at the start, are used when you have an output which when "OFF" is just high impedance, or an open circuit, and when the output is exerted, it pulls "LOW" when it wants to be logic "ON". This allows you to interface with various voltage levels too, and is common for older circuitry - often referred to as Open Collector outputs.

In the case of inputs such as Reset, these are active LOW, which for noise-immunity reasons require a "HIGH" voltage to be "OFF", and when the pin is detected low (usually from a strong external current sink, or just power-off) then in this case the reset mode would be activated. 

edit: Those schematics are pretty whack, and I can see why you are confused. In the second one, the reset is held low, but weakly, and the input signal is a "NOT reset-wifi", so if you do NOT want to reset the wifi, this signal has to be held high by something external. I guess the external signal may not be able to drive low, so the pull down resistor is there to ensure it goes low and holds the wifi in reset, until actively pulled high again.

edit2: The use of these resistors is basically related to what the device is interfacing with, the use-case scenarios (like what happens during a reset), and what the datasheet recommends. Except for what the datasheet recommends, the rest at optional/based on that application's requirements.