Difference between TTL I/O type vs Schmitt trigger I/O type
Regarding your first question, when the input voltage is between the valid regions for a logic 0 and a logic 1 then the output cannot be specified. It may be a 1, it may be a 0, it may be at some voltage in between a valid 1 and a valid 0.

For the second question, the voltage switching points at the input to a Schmitt trigger are different depending on whether the output is currently a 1 or 0 (for the non-inverting case). When the output switches from a 0 to a 1 the voltage thresholds shift downward, favoring the 1 state and making it more difficult to switch back to a 0. The reverse happens when the output switches from a 1 to a 0. The benefit is that noise on the input signal won't cause glitches on the output.
A Schmitt trigger is also often used to "sharpen" a slowly changing input signal.