Two cooks following the same recipe at the same setting can get different results because the pan is not a neutral container. It determines how heat arrives at the food and how steady it stays.
Conductivity decides evenness
A burner heats a small area, and the pan has to spread that energy across its whole base before the food ever feels it.
Metals differ substantially in how readily they move heat sideways, and a poor conductor leaves a hot ring above the flame with cooler metal around it.
That is why the same pancake browns in a circle in one pan and evenly in another, with no change to the burner or the batter.
Thickness and mass govern stability
Heat capacity describes how much energy a pan stores, and a heavy base holds a large reservoir that food cannot drain quickly.
Dropping cold ingredients into a thin pan pulls its temperature down immediately, so browning stalls and the food releases water and begins to steam.
A thick base absorbs that same load with a small temperature drop, which is the entire reason searing works better in heavy cookware.
Responsiveness trades against stability
The same mass that resists cooling also resists being turned down, so a heavy pan continues cooking well after the flame is reduced.
Light pans respond almost instantly to a change in setting, which suits delicate work where a few seconds of excess heat spoils the result.
Neither property is better in general, and this is why a working kitchen keeps both rather than one excellent pan.
Surface behaviour is a separate variable
Bare metal allows food proteins to bond to the surface, and that bond is what creates the browned residue a sauce is later built from.
Non-stick coatings prevent that bonding by design, so they release food cleanly and leave almost nothing behind to deglaze.
Seasoned iron sits between the two, carrying a polymerised oil layer that releases reasonably well while still permitting browning.
Shape controls evaporation
A wide pan exposes a large surface to the air, so liquid leaves quickly and a sauce concentrates rather than simmering indefinitely.
Tall narrow pans hold moisture in, which suits long simmering where reduction is not wanted and the ingredients need to stay submerged.
Sloped sides allow tossing and let steam escape from the edges, which is why stir-frying and stewing are done in vessels of such different geometry.