What's the distinction?
Say Zimmerman's lied about a bunch of stuff to benefit him in life. Maybe he cheated on tests when he was in high school. Maybe he lied on college admission papers. Maybe he lied on his resume. Maybe he lied to his boss. Cheated on his wife. Lied to the judge about his finances. All these things go to prove that Zimmerman is a liar and will do what it takes to help himself in a tight spot. None of it means he lied to the police about what happened the night in question. If the State has evidence that disproves Zimmerman's story, then the burden is on them to put it on and show the jury Zimmerman's a liar. Maybe the wounds dont match up, maybe there's an eye witness, maybe the angle of the bullet trajectory. All of that can show Zimmerman is lying about the murder. Every other bad thing he's ever done in his life does nothing to show Zimmerman lied on the night in question.
He lied to the judge. I agree that's serious. That's why we have the crime of perjury in our country. If they want to charge him they can, and then all those statements are highly relevant to prove that crime. It does nothing to show he's lying about the murder other than to ask the jury to jump to conclusions, speculate and make assumptions. Thankfully, our criminal justice system requires hard evidence to convict.