The sizes are only recommended so deviating slightly won't be a killer (other than drill.bits having too big a shank to.fit in the chuck). The metal drill size you can generally take as the maximum physical size of drill shank the chuck will accommodate, but not always. One thing to understand is that if you exceed these recommended sizes, on cordless drills at least, you risk overheating the motor and the battery of the tool. This could mean bye bye motor, but is more likely to either see the battery off or at the very least cause the protection circuitry to kick in in order to save the aforementioned motor and/or battery. The bad news, though, is that this electrical protection whilst fitted to modern (I.e. last 5 to 8 years) professional level kit is either rudimentary or completely missing from DIY, Chinese knock-off and older professional gear. So, caveat emptor!
What I have found is that using far too large a drill bit results in often horribly slow drilling with everything getting a bit warm. I haven't cooked a motor yet, but I have cooked batteries (in the days before protective circuitry). The biggest killer was always a combination of underpowered cordless drill, large hole saw (100mm and above) and especially warm flat roofs (2 or 3 layers of torched-on felt over 100mm plus of mineral wool over hardwood plywood).
In case you are wondering , selecting too small (motor power) corded drill then running a massive oversized drill bit in it will also potentially result in a cooked motor. Smelled a few of those in my time. Once again the manufacturers generally fit a chuck to suit the largest metal drill bit the motor can sustain without overheating the the motor. It isn't arbitrary (unless, of course, you are buying Chinese stuff where seemingly anything goes)
One other point to note; many DIYers (and not a few trades) seem to always want to select the maximum speed the drill will run at, a practice which can blunt bits and even reduce cutting rate This isn't always the best - always match the drill speed to the diameter of the tooling