I've seen the word "curd" used in a few South Asian recipes (like, notably, some "Butter Chicken" recipes). In one video, it kind-of looks like it might be cottage cheese (or something like that), which would make sense given what "curd" means to me in the US (like, "curds and whey"). However, it also may have just been plain yoghurt, or something else.
I've looked through a couple of recipe books and I see no mention of it. For the recipe in question I'm pretty sure that yoghurt would work just fine, but I'm curious.
In the recipe in question, the "curd" is put in a food mill with some garlic, ginger, and peppers, and some spices. Thus, with either cottage cheese or yoghurt, it'd end up more-or-less the same, with possibly more fat and acidity from the yoghurt I guess. (It's a marinade for the chicken so it doesn't seem critical to me.)
At the restaurants where I have made butter chicken, we used a very thick yogurt to make it. A Greek yogurt (or even sour cream) would work, provided it wasn't excessively sour.
If you're feeling more DIY, you could strain some regular yogurt through a coffee filter to make it a bit thicker and use that.
Curd is homemade Yogurt, we call it Dahi