What is it called when something is described as something completely opposite from the truth?

What is it called when something is described as something but the something is in fact anything but that something?

For example :

• a strong man who calls himself a weakling
• a purple man who calls himself a red man

Contradictory or opposite comes to mind but that is not what I am looking for.

Its a bit like politicians say they represent the people when (in some ways) they don't.

Or another example might be the Republican Party in the US. The word republican probably had a certain meaning when it first started but now it probably has an opposite meaning (and probably many other meanings). The word that has evolved over time to possibly mean something else.

I hope that explains it, but maybe some comments/questions might help me clarify it further.

Perhaps you're looking for "misnomer"?

This would apply to your example of the "Republican" party, at least, where a name that used to be descriptive no longer is.

It could apply to the other examples, as well, although those are more about the act of lying than about a misleading term.