Raise your hand if you'd like to be better at climbing. Yeah. Me too.
I've spent an unusual amount of time working with beginners, to help them improve at climbing. I've also worked a lot with (what I would consider to be) intermediate climbers, so they can get better. I've certainly watched advanced climbers do their thing, but I'm not sure how much I have to offer to them.
My quick observation about climbing, existing skill levels, and improvement is this:
At a most basic level, a climber needs to build movement skills, and needs to learn to belay. Strength is not a big part of this equation, because most "easy" climbing is not a function of strength, but technique. Fortunately, just by building this base of movement skills, the climber will get stronger.
I would expect a beginner climber to learn the basics of hip rotation, flagging/smearing, and climbing with straight arms. Everything else is icing on the cake.
As far as technical skills, a beginner should be able to top rope belay.
Once the climber has mastered the above skills, they're a solid candidate for being an intermediate climber. Movement skills will be refined, especially as climbs take the feet farther and farther out from under the climber. (Not necessarily due to steepness, but due to large horizontal movements.) This will place more stress on the upper body, so the climber will keep getting stronger. The climber will get comfortable with side pulls, gastons, heel hooks, and all those fun things. (Including all the movements we have to do that defy categorization. The beached whale, anyone?)
Our climber will also be picking up additional technical skills. The climber will learn to lead belay and lead climb, and starts getting into the mental game that permeates this strange sport.
So far, I've not mentioned anything about grade. How hard does our climber need to climb to be considered intermediate?
I don't know. I am of the opinion that if they can handle the above technical skills, they'll find themselves climbing harder grades. I'm hesitant to put a grade on any stage for many reasons, but mostly because focusing on technique will carry us all farther than focusing on grades.
An easy example is the mythical grade of 5.12. Most people don't think they are STRONG enough to climb 5.12, but I think most people just are not good enough at climbing to climb 5.12. The strength comes as they improve their technique. If someone just tries to get really really strong, without focusing on their technique, they'll never get anywhere.
Phew. Brain dump. All done.
Oh yeah - that third level? That's advanced climbers. Not sure what their defining characteristics are, but I'll let you know when I get there. :)