The best way to tell the difference is to look at the effect lighting has on your eye area.
Dark circles appear when you see physical pigmentation in the under eye area. So no matter what lighting you’re in - whether the light is from above or straight on - you’ll notice a darkness in your under eye area.
Puffy under eye bags appear differently.
If the light is coming from the front you won’t see any darkness, but if the light is from overhead, because of the physical indentation caused by puffiness, it will look like you have dark circles.
And it’s important to know which one you have because treating eye puffiness will reduce the eye bags but if you have dark circles it won’t affect it.