Logically there can be differences depending on the type of value that you are comparing and language you are using. For example:
x == false implies x != true, but x != true does not always imply x == false because x can also be some nonsense value.
1 + 1 = 3 is both == false and != true.
7 > cat is neither == false and != true since it is nonsense.
x = null is != true but is not == false.
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