You’re right, but one thing that can be said is that despite both of them being well known for their influence in the horror genre, they are not exclusively horror content creators. For example King has written quite a few works in the Fantasy and Dystopian genres. While Carpenter has done more in the Sci-fi and action genre.You're right. They reference him (as he is referenced in countless movies and tv). It just made me think of an interview where Carpenter emphasized he is not meant to actually represent King, just a similar writer. He also writes quite different novels from King. Even books of King, like Revival, which have strong Lovecraftian elements, are not Lovecraftian as a whole. The Sutter Cane books give the impression they are completely like Lovecraft's. Also the movie's title is like a Lovecraft title, close to At the Mountains of Madness.
Eyes of the Dragon and The Long Walk are to King what Big Trouble in Little China and Assault on Precinct 13 are to Carpenter.
I think the defining points of their storytelling styles is that King uses wit to describe almost everything regardless of how disturbing it is, and Carpenter tells his stories more through over the top cutting-edge practical effects.