The various forms of assent range from "getting to the top by whatever means" through "betas" to a true "on-sight" and even the ridiculous "free solo". There are plenty of records still to be set on this route. An on-sight is pretty much inconceivable on a big wall (no prior knowledge, just show up and climb) but clean assents (no falls on any pitch) will happen one day.
The history of the Yosemite decimal system speaks to the increased ability of modern climbing. A 5.10 free route was once considered the hardest thing humanly possible. Now we have 5.14 as 5.10, with modern rubber, is easy. I've seen noobs do 5.10a top-rope (no fall risk) on their first day. Not everyone can, but most noobs can battle their way up a 5.8 once they get the hang of things. A 5.10 near the ground is a totally different beast than the same pitch up on a wall, but concepts such as "exposure" danger and distance are not part of the yosemite decimal system, only technical difficulty.
If you really want to scare yourself, look at aid climbing standards. Aid climbing is where you use devices to actually pull yourself up the rock. This is how Dawn Wall has been tackled since the 70s. Aid pitches are graded from A0 to A6 based not so much on difficulty but fall danger. A0 is basically a 5.xx route with some pulling on gear. A3 means many not-solid pieces in a row, resulting in 10-20 meter fall potential. A5 means only the belay will hold a fall, so you could go 70+meters before the rope catches. Basically, A4 and above means fall = hospital. The legendary A6, which I doubt exists, means even the belay stations won't hold = certain death.
Oh, and "big wall" means climbing that could/should involve sleeping on the wall. But elite climbers regularly flash up well-traveled yosemite walls in hours, They are still big walls.