Wattage is just the amount of power applied to the coil... Temp control limits the power applied by cutting the power once the desired temp is reached, then re-applying/balancing the power to the coil to maintain the desired temp.
In Temp Control mode, if you have the power set to 200W, and the temp only requires 50W, it will heat up fast (applying 200W), then turns the power off/on rapidly to maintain the temp. If you have it set at 50W, then the heat-up will be slower, but the controller will not have to pulse the power on/off to maintain the temp.
Does that make more sense?
In Wattage mode, the power you select (20W, 50W, 200W, etc) will be applied to the coil... and over-powering the coil will cause it to pop at worst, or burn up your coil/cotton at the very least. This is why I suggested you start low and use trial-and-error to find your sweet-spot. The same applies to TC mode... start at a low temp and adjust your temp higher and higher until you find the desired level. If it heats up too quickly, or you see the mod is having to work hard to maintain the temp, back off the Wattage. If you find raising your temp has no effect, then you may need to apply more wattage in order to reach that temp?
The stamps on the coils are just for reference... like a guideline, and make no difference whether in TC mode or Wattage mode. Most of those stamped ranges are determined using zero-nic and an unknown PG/VG ratio (or just arbitrarily given, based on the Ohm-rating of the coil), so they will not be definitive ranges for the juice YOU are using. Like I said, I have one coil that says 30W is the recommended low/minimum, but I find my juice is great at only 18W... 30W would burn it to a crisp! Another coil I regularly use says 15W-40W as the recommended range, and I've used it at 50W with a high VG juice for fantastic flavor and vapor...