The episode you seem to be referencing is Book 2 Chapter 1: The Avatar State, when Avatar Roku's spirit gives Aang a crash course in the meaning of the avatar state. We get a quick demonstration of the power of the avatar state when we see it invoked by Avatar Kuruk to bend a gigantic wave, Avatar YangChen to cause a gale force gust, the fire nation avatar before YangChen to cause a volcano to erupt, etc.
Technically, you would be right to say anyone who has mastered bending their native element could create such feats. I don't believe the term bending master has ever been formally defined in the show, though evidently it implies great skill in bending. Whether that implies the ability to bend X massive amount of the element at once or perform an incredibly intricate move is not said and there is no hard cutoff. It evidently is opposite that of a novice, though, who'd be getting a feel for the fundamentals by pushing/pulling their first ripple of water or generating a small puff of flame, so it makes sense a demonstration of how much of an element could be bent at once is a signal of mastery.
The thing is that like the martial arts, the bending is based in proficiency that gets better with experience and time. People continuously get better with practice but those skills do not necessarily scale linearly; e.g. bend rock -> bend bigger rock, Bumi at the ripe age of 112 has the ability to earthbend by tilting his head.
Mastery is more or less just a sign of proficiency or title of respect and there is no upper cap on it. Eventually a waterbender may achieve the skill needed to bend a wave like Kuruk, but the skill being demonstrated in the scene is the ability to tap into, as Roku says, skills, powers and experiences of all past lives of the Avatar. The ability to use skills yet to be learned from scrolls yet to be read in one's current lifetime.
It is nice that the scale of the feats shown to Aang are greater than any single feat by a non-Avatar otherwise, but the true special quirk of the Avatar is not the mastery of one's own bending element. The thing that any random bender cannot do but the Avatar can is bend more than one element. Kuruk is shown bending a massive wave, but could have just as easily bent a gale force wind or a giant fissure because we see previous Avatars doing so.
I've only watched Avatar: The Last Airbender, never Legend of Korra, and am not familiar with most of the comics that exist around the series, perhaps a better answer is given elsewhere.
