The jury doesn't send people to jail: they vote guilty or not guilty and the judge decides the sentence, expect possibly in death penalty cases. And, in the U.S. at least, the jury isn't allowed to be told what the possible sentence is.
Close, but not *quite* it.
Jurors are finders of fact. They determine what happened, "as a matter of fact.", so to speak.
Judges are finders of law. They determine a conclusion, "as a matter of law."
Judges can also be finders of law, where there are no jurors and in other situations.
So a juror can find, as a matter of fact, that someone intended to and actually killed someone else, and thereby committed homicide. A judge can find that as a matter of law the act of homicide is a punishable offence, and compel this person to incarceration for a requisite period of time.
In that sense, jurors do indeed determine the presence or absence of culpability, or wrongful guilt.
Sentence can vary depending on the facts found by the jurors. Jurors can determine whether there was intention to murder, whether it was planned, an act of emotion, or self-defence.
What jurors find, in other words, is not strictly limited to the presence or absence of guilt.