Schmitt triggers hysteresis symbols
According to IEEE Std 91, Standard Graphic Symbols for Logic Functions, the correct way to indicate an input with hysteresis, such as for a Schmitt trigger, is:



So your third and fourth examples, which show the hysteresis symbol mirrored left-to-right, are not correct.

The correct way to indicate an inverted output is with an open circle:



So it looks like your first image is correct for a non-inverting buffer with hysteresis at the input, the second image is almost correct for an inverter with hysteresis, and your third and fourth images are incorrect.