It indicates importance of the topic and hardness of disgreement.

Tabs vs spaces - people disagree but usually can adapt to the team if needed.

Use java1.4 for green-field web app - hard disagreement for many, looking for new job is more attractive option.

Difference between the two is that hard disagree means you won't be able to change their mind.

Or "should not" change their mind. If I hard disagree, then I should not change my mind, because I see no valid reason, and both my experience and reasoning are solid to the degree I am certain the arguments presented can not develop into a valid reason to change my mind. "Hard disagree" may signify being certain. I then am responsible, for my own sake and wellbeing, of being right in relation to reality, or reality will simply hard disagree.