Of the two rank systems Tenhou uses, R is the more precise. Players start at 1500 and either fall or rise based on their results and the R rating of their opponents. This number changes every match, while the kyu and dan ranks use experience point systems that force the player to win more often than they lose in order to advance to higher ranks.
Tenhou's matching is broken up very evenly by skill level. The general lobby is for the kyu ranks and beginners. When you break into the dan ranks, you have the choice of either staying at the general tables with a harsh penalty for losing (it's considered easy prey, so you'd better not lose) or moving on to the lower dan tables, where I have been playing for quite some time.
Likewise, 4th dan and 1800R is the point at which you get access to the high-level dan tables. When you show up at a table with over 1800R, your R is displayed under your name so as to warn other players. If you're both 4dan and 1800R you're also barred from entering the general tables altogether: you are officially too good for the masses. That's what's so cool about this milestone: even reaching 1800R you really feel like you're pretty damn good. It is not a point everybody will get to.
The highest-level tables and tournaments are for players over 7th dan and 2000R, and Tenhou's very best players approach 2300R. (In Saki, I believe Nodoka had something ridiculous like 2500.) There is a full breakdown of the number of players at each rank, their average R, and other stuff on Tenhou's ranking page.
Down at my level there are 17,275 players at third dan and 10,384 at fourth. As you go up the rankings, the number of players gets slimmer and slimmer: 1,300 players at 7th dan, 400 at 8th. Only three players have ever achieved Tenhou's top rank.
As you might have gathered, the ranking system on Tenhou gets really brutal. In the early dan ranks, losing costs you as many experience points as a win, so a 4th place finish cancels a 1st place finish. At third dan, losing starts to cost you slightly more than winning. This gap increases as you move along, so the only way to advance in the ranks is to really get better at the game. The climb gets steeper and steeper as you go.
Aside from its ease of use and simplicity, this is one of Tenhou's strongest points. All Tenhou is doing is putting you against progressively stronger players and showing you if you are actually getting better at the game. Frills are minimal.
Compare this to the flashier Janryumon. If you plug away on Janryumon for long enough, you'll definitely ascend the ranks, because the game doesn't necessarily count every loss against your rank. There is an R score, but it crawls upwards at a snail's pace because JRM's advancement is designed not to force you to improve at mahjong, but to keep you playing mahjong. The items, the events, the rank progression, it's all about just keeping your ass in the chair. It's very successful, but if you're serious about improving I see no substitute for what Tenhou offers.
So I'm proud I got to 1800R, and hopefully things will go well from here and I'll be able to take 4th dan. I'm confident in my skill, but this game is cruel. Nothing is guaranteed.