What's the difference between hardheaded and mulish?

Hardheaded

Definition:

Example Sentences:

Definition:

Example Sentences:

(1) In the circumstances, you do have to marvel at that mulishly self-regarding "for any offence caused" – the classic non-apology apology typically proffered by those with a belief in their own absolute probity, which is as unshakeable as it is misplaced.
(2) ''I wouldn't call her ridiculous,'' he said, mulish.
(3) The result had everything to do with Labor’s dreadful lies and nothing to do with mulish voters stuck in the old economy not buying the mantra of exciting times that could be made more exciting if only corporates paid less tax.
(4) Yet on the Labour leader clings, his mulish cabal citing the mandate given by his landslide election in a leadership contest that now feels like it happened about 12 years ago .
(5) Before the “dream team” of Kevin and Julia fractured into mulish remonstrance, Gillard maintained sufficient trust to be able to wander in and out of Kevin’s gumnut room at will.
(6) "Basically, I've checked all other possibilities," he is saying mulishly, "and it's come down to the calculator."