Yogurt appears throughout Indian cooking in roles that European cooking assigns to cream. The two behave very differently in a hot pan, and the techniques around yogurt exist to manage that.
Yogurt brings acidity that cream does not
Cream is essentially fat suspended in milk with near-neutral acidity, so it enriches without changing the flavor balance of a dish beyond adding body.
Yogurt is acidic from the lactic acid produced during culturing, so it enriches and sours simultaneously. A dish built on yogurt has its acidity supplied by the same ingredient that supplies its body.
This is why yogurt-based preparations often need no separate souring agent, and why substituting cream for yogurt leaves a dish tasting flat as well as different.
Heat breaks the protein network
Yogurt's milk proteins are already destabilized by acid, and heating pushes them further, causing them to clump and separate into curds and watery whey.
Cream resists this because its proteins are not acid-destabilized and because its high fat content buffers them. It can be boiled into a sauce without splitting.
Indian technique manages the split rather than avoiding it
Whisking yogurt smooth before it goes into the pan breaks up the protein network in a controlled way, so there is no intact gel left to seize into visible curds.
Adding a small amount of a starch such as chickpea flour gives the proteins something to interfere with, physically obstructing them from clumping together as they heat.
Adding yogurt off the heat, or in stages with constant stirring, keeps the local temperature low enough that the proteins never reach the point of aggregation.
Fat content changes the tolerance
Full-fat yogurt is markedly more stable in cooking than low-fat, because the fat interferes with protein aggregation in the same way it does in cream.
Most American supermarket yogurt is available in both, and choosing low-fat for an Indian gravy is one of the more common causes of a split sauce in a US kitchen.
Strained and unstrained behave differently
Greek-style yogurt has had whey removed, so it is thicker and contributes more body per spoon, but it is also more concentrated in acid and can dominate the seasoning.
Thinning it with water brings it closer to Indian dahi in both consistency and intensity, which is usually a better starting point than adjusting the rest of the recipe around it.