I checked the Dungeon Master’s Guide. It’s actually:
1 - 4: local heroes
5 - 10 - heroes of the realm
11 - 16 - masters of the realm
17 - 20 - masters of the world
Heroes of the realm is described as:
By the time they reach this tier, adventurers have mastered the basics of their class features, though they continue to improve throughout these levels. They have found their place in the world and have begun to involve themselves in the dangers that surround them.
Masters of the realm:
By 11th level, characters are shining examples of courage and determination — true paragons in the world, set well apart from the masses. At this tier, adventurers are far more versatile than they were at lower levels, and they can usually find the right tool for a given challenge.
The later sounds much more to me like high level than the former.
