Yoghurt/Yogurt is the result of fermentation of milk by a bacteria. The bacteria reacts with the milk resulting in the texture with slightly tart flavored Yoghurt. Yoghurt is known particularly for it's probiotic characteristic which helps in better gut health.
Curd or Dahi as we know in India is similar to Yoghurt because of the process of fermenting with bacteria. But there is a difference here. Yoghurt could have multiple strains of different bacteria, but the quantity is controlled resulting in a standardized product. Whereas, curd or dahi is generally one bacteria viz., Lactobacillus and it is prepared at home or small to large enterprises, but it can be said that it is not standardized especially when compared to Yoghurt. The density of the bacteria generally varies a lot.
Yoghurt is generally preferred for it's higher probiotic content. Nonetheless, due to the probiotic characteristic of curd or dahi, we should think of including it in our daily diet for improved gut health.