NB: this is an answer about (wheat) bread. Other baked goods made from other doughs and batters, or bread made from other types of grain (specifically rye) might have additional factors.
The clear difference is the taste. There aren't any interesting chemical effects which would disappear if you don't use the yogurt; in fact, there are many more recipes with milk alone, and they work very well. So the obvious purpose is to have a sourer taste than what you can achieve with milk alone.
The difference might be minimal if you buy industrially made yogurt adapted to western tastes, but it will be very noticeable if you make your own yogurt and prefer it on the strong side. You can even imitate a sourdough taste without going to all the trouble of keeping a starter around. This is especially handy when you always have a supply of homemade yogurt, but only bake bread rarely.
One could of course take this to the maximum and bake a recipe with yogurt only. This is indeed what many people do. But there are three reasons to also make mixed recipes:
- there are people who don't want the taste of full-on yogurt-only recipes, and prefer to milden it.
- logistics. When you have a cow or get scheduled deliveries of (raw) milk, you frequently face a situation where you have too much milk which will spoil soon, while there is not much yogurt left. You could either spend time on making more yogurt, or kill two birds with one shot, by baking a bread in a way that balances out your dairy supplies.
- acid inhibits yeast growth and does wonky things with gluten. The effect is not strong enough for the bread to fail altogether, even when the whole liquid is a very sour yogurt, but if you either don't want to wait for the slower rising (or don't know that it's slowed, do your baking by time, and are disappointed when your dough has risen little at the two hour mark) or don't enjoy the texture of somewhat acidified dough, an obvious solution is to not use all yogurt, but add milk.