The AHC/AHCT Designer's Guide says:
When there are slowly rising edges at the input, oscillation within the device can occur as a result of high voltage amplification, high cutoff frequency of the transistors, and parasitic components coming mostly from the package. To suppress this oscillator, a kind of Schmitt-trigger circuit has been integrated into the input stage. […] The switching thresholds on the positive and negative edges at the input differ by about 200 mV and the input circuit has the hysteresis characteristic that is typical of Schmitt-trigger circuits. Transfer characteristics of AHC devices are shown in Figure 2 …
Hysteresis in the input circuit is intended only to process reliably signals that have a slew rate of <10 ns/V. With a signal swing of 5 V, this corresponds to rise and fall times of about 50 ns. If signals with considerably longer rise and fall times are processed, the specially developed Schmitt triggers, such as the SN74AHC(T)14, should be used. These components have a considerably larger hysteresis of about 800 mV at VCC = 5 V and, therefore, allow processing of very slow edges without any problems.
