But what does the difference mean?
On a long rest does a level 1 fighter gain 1d10 HP, 10 HP, or 1 HD which requires another rest to gain HP?
This is just my guess from my reading of the article, but: after a long rest, a 1st-level fighter regains 1 Hit Dice. When he takes a short rest, he can expend that Hit Dice to regain 1d10 hit points.
At higher levels, it is not clear:
1. What is the maximum number of Hit Dice each character can have. A number equal to level seems likely (i.e. a 9th-level character can have a maximum of 9 Hit Dice), but any fraction or multiple of level (half level, twice level, etc.) could also be possible.
2. How many Hit Dice are regained per long rest. Most likely, it will be a fraction of the maximum Hit Dice (one-third, half) so that it will take a character a few days to completely recover from being brought down to 0 hit points.
Another point that seems very likely at the moment is that the average number of hit points that can be regained from a character's maximum Hit Dice will be less than the character's full normal hit points. This means that a character's hit point reserve, in the form of Hit Dice, will be far shallower than in 4e. So over the course of an adventuring day, you might see a character expending all his Hit Dice to regain 50%, 75%, or (with a series of lucky rolls) 100% of his full normal hit points before he needs rest for at least a few days. That would address the criticism that 4e characters recover hit points too quickly, both in terms of a single adventuring day (where it is theoretically possible, though unlikely, to go from full hp to 0 hp and back to full hp two, three or more times per day) and from a day to day basis (because all hit points and healing surges are recovered after an extended rest).