HOUSTON — It was a face that haunted many people in the nation’s fourth-largest city: The police sketch of the unshaven white man who witnesses and the authorities said had opened fire on a black family in a car the day before New Year’s Eve.

A second grader riding in the car with her mother and three sisters — Jazmine Barnes, 7 — was shot and killed. And the man in the sketch — thinly built, in his 30s or 40s, wearing a black hooded sweatshirt, driving a red pickup — became the focal point of what appeared to be a racially motivated shooting that rattled black residents, elected officials and civil-rights activists in Houston and around the country.

“Do not be afraid to call this what it seems to be — a hate crime,” Representative Sheila Jackson Lee, a Houston Democrat, told hundreds of people at a rally last week near the site of the killing.

But it has turned out far differently.

On Sunday, the authorities charged a suspect with capital murder who is not the man in the sketch. He is a 20-year-old African-American man named Eric Black Jr. Investigators with the Harris County Sheriff’s Office said that Mr. Black acknowledged taking part in the shooting, and that Jazmine’s family’s vehicle may not have been the intended target.