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I think the confusion lies with the term Hit Dice.  It's a subtle mention at character creation and that's about it.  For vets the idea of Hit Dice isn't new, but for others it might escape notice.  I actually had to  stop and think about this for a moment.

Hit Dice are the dice you roll each level to gain hit points.  When you roll dice for healing through short or long rest or other means, you roll a die (or dice) based on whatever die you rolled to gain HP in the first place (Hit Dice.)  So a Rogue rolls a D6 to gain new HP max when they level.  The D6 is a Hit Die.  If you're second level, that's another D6 added to your max HP (2D6, so it would be 2 Hit Dice total.)  This would mean the Rogue has 2 Hit Dice to use for healing.  To get the Hit Dice used back, the Rogue needs to take a long rest first - which would be 6 hours of sleep in an 8 hour long rest period (including 2 hours on lookout.)
 
At least this is how I interrupted it all.  If I'm wrong, someone please correct me because I want to make sure I understand this as well.

They just need to be explicit on its use, i.e. hit dice value for the class, hit dice roll for generating hit points, or hit dice roll for healing and how to recover the use of them.

They made very poor choices with the naming of this mechanic. The "Hit Dice" are healing surges (4e), just ones that heal a variable number of HP instead of a fixed number. They have no relation whatsoever to Hit Dice (1e through 3.5), other than that characters happen to have the name number of Hit Dice (Next) as they do of the things that 1e through 3.5 called Hit Dice and Next calls nothing (but which many people call Hit Dice, because characters have the same number and size of them as they do Hit Dice, and because that's what they used to be called.)