The difference between "dark chili powder" and "chili powder" primarily comes down to the types of chili peppers used and the resulting flavor profile. Here's a breakdown:
Chili Powder (Regular):

This is typically a blend of ground chili peppers mixed with other spices like cumin, oregano, and garlic powder.1
It has a more general, balanced chili flavor.
The color tends to be a reddish-brown.

Dark Chili Powder:

Often, dark chili powder gets its deeper color and flavor from the use of specific chili peppers, most notably ancho chilies.2
Ancho chilies, which are dried poblano peppers, contribute a sweeter, smokier, and earthier flavor.3
The color is a deeper, darker brown.4
It tends to have a milder heat than some other chili powders.
Also some companies will roast the chili peppers used in the blend longer, to create a darker powder, and a more smoky flavor.5

In essence, dark chili powder emphasizes the richer, smokier notes of certain chili peppers, while standard chili powder is a more general spice blend.