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That's right. You might want to look into the difference between potential difference (measured in volts) and current (measured in amps). When there's a difference between the potential stored in the capacitor (as charge, measured in coulombs, divided by its capacity, measured in farads) and the potential applied, a current flows. It is this current that charges or discharges the capacitor.
To expand on this, the valid input voltage ranges are different for TTL signalling versus CMOS versus LVCMOS signalling. The reason for this is that TTL logic (and the compatible NMOS that followed it) had a lot more difficulty pulling up to the positive rail than down to ground. Modern CMOS logic can pull equally well either way, and it's easier to build a CMOS input stage symmetrically as well. A CMOS output will happily drive a TTL input, but you must use special TTL-compatible inputs with a TTL output.
I would also mention the 74AHC series, which has most of the speed of 74AC but with the drive strength more compatible with 74HC-based designs. Another advantage of CMOS gates in general (but not the ones with TTL compatible inputs) is that they will work on lower supply voltages than 5V, usually down to 1.8V, though a bit more slowly.
@KarlPeters The second, transistorised circuit should consume less power than the first, Zener-only circuit with the higher voltage batteries, and the same amount with the lowest voltage battery. The vast majority of the power goes to lighting the LEDs, and you can tune that by varying the resistor value.
