Jeld wen window balance
I'm sorry to say I can't identify what you need based on these photos. We're going to need to see an undamaged balance removed from the window to get a better idea of what you have. Once it's out, I need to see a clear and unobstructed photo of the top end, bottom end, and whatever clip or hook is at the end of the shoe.
Thank you. This is a bit confusing; your first photo showed a channel balance, but these new photos are showing an entirely different configuration. What you have here is an old style rod balance. I'm wondering if someone repaired this window before you got it and mixed the hardware together.
Either way, we would also recommend a channel balance in this case. These rod balances haven't been made in years. You can use a modern channel balance, but it takes a little handiwork on your end to get functional. I'll share a video guide that explains exactly what's necessary from you to get this project completed. You're going to want to get the weight of the sash, and you'll need an undamaged balance in the same size to accurately measure length. It's not possible to garner size from a broken rod balance due to the way they come apart.