Same scenario but one for each:
Horror: Mom was torn away from me in the darkness, I heard her screams weakening, I ran down the hall to her just as the thing finally smashed her lungs.
Dark: He threw me against the wall, stomped on my shin, and kicked my head four times, then he walked back to my mom. I couldn’t stop him long enough, I heard him throw her back to the ground, she was crying, telling him to stop.
thud
thud
thud
Her voice, now gurgling was growing softer. I finally turned my head, and saw her:
Red. Blue. Black. Purple. Her left leg wasn’t strait. Her arms unmoving. He was just sitting on her while his punches slowly became wetter.
A dull crack.
She breathed a shuddering, wispy, strained breath. Then there was sound no longer.
I’m not great at writing, but I think this illustrates the difference. Horror is generally a bit more style of substance, while dark is generally about themes, and substance. Dark also often cynical in its message.