As a novelist my preference is for what I call an 'active narrator'. The terminology confuses most as they think I'm talking about sentence construction and the benefits of 'active' or over 'passive' voice.
That's not it.
The issue is whether the narrator has a character. Obviously, the technique is common in first person but can also be used in third.
The narrator has no interest in Strunk & White; they simply tell the story using their own words.
e.g. "Becky Sue weren't no kind of mother but she did the best she could with what the good Lord gave her. At the age of thirteen she pushed Ryan out of her belly, and proceeded to drop another sprog every year for the next five years. All them kids had different fathers - Becky Sue had bills to pay and mouths to feed. Some say the preacher, Reverend Kelly, caused her predicament. The Reverend was Ryan's father, and it was him who told Becky Sue that contraception was a sin."
It is obvious that I (the author) am making no attempt to write using my best words and grammar. I'm using the narrator's words.
You guys must have a name for this style of narration.