I believe you guys have had that discussion on here before already, haven't you?
I don't think there is an official "distinction," since it's not really an official stat in any way, is it?
But I do understand it... when you're playing every night, you're part of the team's grind -- the travel, the back-to-back nights, all the time away from home, etc. The only reason "50 in 50" matters at all is because of the "Holy shit! He hasn't slowed down yet this season!" factor as the season progresses. It's not really relevant beyond the fact that it's sort of cool for that reason, and an injured player, through no fault of his own, isn't following the same pattern (and may also be more rested, for whatever it's worth).
It's for the same reason why a guy who scores 50 goals in the final 25 games of one season and the first 25 of the next will be equally ignored, even though he has hit 50 in 50. It's really no less remarkable, but it lacks that doing-it-uninterrupted-from-the-start element. Or a guy who scores 10 goals in two sets of four consecutive games (with one game of zero in between) will get ignored relative to the guy on an 8-game goal scoring streak with 8 goals.
None of the distinctions really matter beyond their actual contribution to the season, they are just noted for fun more than anything.