In fact, the burden of proof is important for everyone and can sometimes lead to results that, on the face of things, seem very weird indeed.
Remember O. J. Simpson? He was acquitted of murder by a jury and then a couple of years later found liable by another jury for wrongful death. That seems inconsistent, to say the least, but in fact it makes perfectly good sense when you realize the first jury was a criminal jury and the second was a civil jury.
In a criminal case the jury (or judge of there is no jury) must be convinced to beyond a reasonable doubt that the accused is guilty. The jury must be sure of guilt. That's the criminal burden of proof.
In a civil case the jury (or judge if there is no jury) must believe the defendant is probably in the wrong. That's the civil burden of proof.
Between probably and being sure there is a big gap.
So if both juries in the O. J. Simpson case thought he was probably guilty of murder the criminal jury would acquit and the civil jury find liability. And that's likely what happened.
Of course if a criminal jury convicts that means they are sure an accused is guilty; that means a civil jury should always find liability.