The graphs are often found for schmidt rigger inputs, because these are also for not so clean signals, like slow rising. Normal logic input can be a bit similar, but usually without the hysteresis.
There is usually no extra current when there is a clean logic signal, like < 25% and > 75% of the supply. How much current and from what voltage level it starts seem to vary between units. Thus the rather large difference between the typical and maximum numbers. The logic chips are usually cheap and thus not tested very well for parameters that most of the time don't matter. If critical in some applications (e.g. use for level shifting in a power sensitive application) it can make sense to check the parts (or at least some from the same batch) upfront.
It is interesting to see the curve for AHCT14 to be really shifted to lower voltages.