Luta Livre. That's named I've not heard mentioned in a while. From everything I've ever known, Luta Livre was people doing BJJ no-gi, just not at the same level perhaps as the Gracies themselves. Of course, that was back in the day.

Now everyone trains no-gi and everyone includes striking. In other words, its something new, now called....uh, wait a minute it's coming......OH YEAH, it's called...MMA.

Now having just checked out the youtube clip, that doesn't look any different than anything currently being done by either camp. To say that there are two completely different "styles" and methods would be inaccurate.