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There is a difference in the schematics, the one in post #5 uses only the Schmitt threshold of the inverter to decide the point where the discharge MOSFET turns on, as soon as the voltage drops below the threshold, the MOSFET turns off again. The voltage is decided by the difference in +Vth and -Vth, the hysteresis of the inverter.
In the post you linked to, there are two comparators to decide the upper and lower thresholds and a flip-flop that enable the discharge between those voltages. The operation is similar but not identical. It isn't clear what the difference is between 'Q' and 'Qb' but I would guess they are essentially the same.
For clues about how it works, take a look at the data sheet for the NE555 which works in much the same way. It doesn't use a current mirror but if you analyze how the discharge circuit works you will see it is similar. Most RC oscillators (here R is a current source rather than a resistor) work in the same way, charge a capacitor, when it reaches a threshold, discharge it and repeat. The ramp is a consequence of the charge/discharge cycle on the capacitor and isn't in itself used in clock generation, it's the cyclic period that matters.
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