The difference in the making of yoghurt to produce carbonated (like Kefir) vs non-carbonated yoghurt

A curd is a transitional element obtained, once milk starts to coagulate, the other being a water substance called whey. These are separated and cheese can later be made from the curd, via the addition of other ingredients, such as rennet. Or in the case of cottage cheese and paneer, an acid.

Yoghurt is a finished product, produced by by heating milk, then adding a live 'starter' culture. It's then kept at a stable warm temperature for a number of hours, followed by cooling.

I think for Indian recipes you should in general look for an unstrained, set yoghurt. There are other factors that determine the final taste and texture of the yoghurt (the bacteria, the type of milk, length of fermentation, …) but you may not have much choice w.r.t. other factors than these two:

Production process: Set yoghurt is yoghurt that's made the traditional way, it's fermented in the pot that it's sold in. Stirred yoghurt on the other hand is fermented before being packaged; it's a more industrialized production process which is cheaper, but results in a more sour, thinner yoghurt. Stirred yoghurt has a smooth, pourable consistency; whereas set yoghurt is firmer. I got a bit confused when I was using stirred yoghurt the first time I tried making raita and the recipe told me to whisk the yoghurt till it was smooth. The pretty sour taste of the yoghurt also didn't go well with the spices, and the juice from the cucumbers made the already-thin yoghurt too watery. You could try fixing both problems by straining the yoghurt a bit and adding sugar, but it's better and easier to just buy set yoghurt. The yoghurt's packaging might say explicitly what type of yoghurt it is, but if it doesn't or you don't understand the language: avoid yoghurt that comes in “milk carton”-like containers, that most definitely means it's stirred yoghurt. A plastic pot doesn't mean it's set yoghurt though, but it's a better bet.

Thickness: Strained yoghurt (like “Greek-style yoghurt” in Europe and the USA) is yoghurt from which the whey has been removed. It's pretty thick and sometimes also referred to as “yoghurt cheese.” In India it's used for example in the dessert Shrikhand, but if a recipe doesn't specify that you should strain the yoghurt, you should assume it's unstrained or briefly strained. Wikipedia says: “In south Asia, regular unstrained yoghurt (dahi), made from cow or water buffalo milk, is often sold in disposable clay pots. Kept for a couple of hours in its clay pot, some of the water evaporates through the clay's pores. But true strained yoghurt (chakka) is made by draining dahi in a cloth.” Should you really only find strained yoghurt, you can probably just thin it back with water or milk.

I should maybe add I don't have first-hand experience with what yoghurt from India tastes like, but I've observed that the ethnic shops in my area and one Indian take-away where I could peer into the kitchen all sell/use the exact same brand of yoghurt, which is an unstrained, set yoghurt with a mild (not too sour) taste.