Vout will switch to (almost) supply voltage and 0V, depending on input level.
Once the oscillator has stabilised, the input voltage will probably range between about 1/3 and 2/3 supply. Each time the cap charges or discharges to the input switching threshold, the output will change state and swap between charge and discharge.
The other circuits are not equivalent as the first stage is an inverter, then with a second inverter added. There is no overall inversion so it will stay in one state or the other rather than oscillating.
The feedback resistor would have to be moved to the output of the first stage to make that an equivalent; the added inverter is then redundant.