Home cooks who cannot reproduce restaurant results often blame the burner. The pan is usually the larger factor, and the reason has to do with stored energy rather than delivered power.
Heat capacity is what the pan supplies
A pan holds thermal energy in proportion to its mass. A heavy cast iron or thick steel pan at cooking temperature contains a substantial reservoir of it.
When cold food lands on it, that reservoir supplies energy immediately, so the surface temperature falls only slightly. A thin pan has almost nothing stored and drops sharply.
The burner then has to make up the difference, and burners deliver heat far more slowly than a hot pan releases it.
Why the drop determines the outcome
Browning reactions need a surface above the boiling point of water. If the pan falls below that, moisture leaving the food cannot evaporate fast enough and pools instead.
Once liquid collects, the food is being boiled rather than seared, and it will not brown until that liquid has gone. By then it is usually overcooked.
This is the whole explanation for vegetables that go grey and limp instead of taking colour, and it is not fixed by turning the flame higher.
Where thin pans are the right choice
Responsiveness is the opposite property, and sometimes it is what is wanted. A thin pan follows the burner closely, which suits anything that burns easily.
Tempering whole spices is the clearest case, since the cook needs to remove heat within seconds of the spices reaching their point. A heavy pan keeps cooking after the flame is off.
The traditional Indian kitchen holds both, a light tempering pan and a heavy griddle or kadai, rather than treating one as generally better.
Why preheating is longer than it feels
A thick pan takes minutes to reach an even temperature throughout, and the surface can feel hot long before the body of the metal has caught up.
Adding food at that point empties the surface heat immediately, because there is no reservoir behind it yet, and the pan behaves like a thin one.
The practical rule is to preheat noticeably longer than seems necessary, and to test with a drop of water rather than by holding a hand above the pan.
What conductivity adds separately
Mass determines how much heat the pan holds, while conductivity determines how evenly it spreads. Cast iron is heavy but conducts slowly, so it develops hot spots over a small burner.
Aluminium and copper conduct quickly but are usually thin, which is why clad pans combine a conductive core with heavier outer layers.
For Indian cooking specifically, mass tends to matter more, since most techniques involve adding wet ingredients to a hot pan repeatedly across a single dish.