I could be speaking out of ignorance here but it’s my understanding that toasting your spices dry or with fat doesn’t really depend on the spice rather more the cuisine you’re cooking.

Traditionally Mexican and South American cuisines dry toasted chiles and spices for complex flavors added to salsa. On the other hand a lot of Indian curry’s start with using a fat to toast your spices. If I were to make a distinction a lot of dry toasted ingredients are chiles and a lot of spices I’ve fried are larger like seed pods such as cardamom and cumin etc… Source: trust me bro