The temp setting uses a sensor to detect the cooktop heat. This heat is what is transferred back from the pan/pot. So it's a fair approximation of the temp of the pan/pot bottom. Use the temperature settings for holding a simmer, setting a frying oil temperature. Holding a simmer in a small pot on a gas stove is tricky and may not be possible depending on the burner. With induction, size of the pot and quantity matters much less as the system monitors the temps.
I've found the temperature settings good for dark roux too as you have more control over how hot the pan gets without exceeding the temp and scorching the dark roux. If you had fine grained controls, it could be good for sugar work. My temperature settings on my unit are usually about 30 degree bumps, too coarse for sugar.
The temperature setting will also protect against a pan simmering dry and over-heating. Temperature setting cycles heat on and off. In an ideal situation, there wouldn't be a difference between bringing a pot of water to a boil by temperature or by power. But in the real world, the power setting works faster because the pan doesn't transfer heat to the water with perfect efficiency so you have a few off cycles in the temp setting comparison. If you set the temp to something like 250, which the pan bottom is probably efficient enough in heat transfer to the water, it will never get that hot, and the unit will pour full power into a pot of water at that temp. Different units may use fuzzy logic to reduce the power as the heat approaches the desired temp so it doesn't over shoot.
When you use a wattage setting, It pours that much wattage into the unit continuously (unitl a "dangerous" temperature is reached, usually in the higher end of the 400s mine maxes out at 464. This is a reasonable choice as you're at or past the smoke point limits of most household cooking oil, and risk some damage to many pots/pans. But for blackening or a steak in cast iron, I'd like to go hotter still.
Think of the wattage settings as equivalent to a burner from low to high. The heat comes in continuously and you regulate the intensity.
There are some situations where the power and temperature settings are indistinguishable, particularly at full power/max temperature.