The whole area is known as Summerlin, and actually you missed one, there's a Summerlin West, as well. Summerlin is 22,500 acres and broken into those 3 master plans. North & West are in the City of Las Vegas, while South is part of unincorporated Clark County.
Those master plans are also broken into a number of smaller communities and some within them as separate entities from the master plan I've marked here with a +.
The Hills South
+Sun City Summerlin
+Red Rock Country Club
I sometimes have to chuckle a bit when someone says "I'm interested in a home in Summerlin", simply because it's a well known name and they don't realize the size. I tell them I think they may want to narrow that down just a bit, it covers a lot of territory.
Hope that helps, and I have a map if you should need it.