Two different radios, two different networks. In addition, they operate on very different frequencies. I could bring a 1990s baby monitor into your house and take out your entire Z wave network and Zigbee would be completely unaffected. Or I could install Wi-Fi boosters and take out the Zigbee network while the Z wave devices would continue to run happily.
They’re housed in the same plastic box, but otherwise from a network engineering standpoint they are completely separate networks. So it’s never surprising if you’re having an issue with one and not the other. 
It’s like parking your motorcycle next to your car in the same garage. It’s not surprising if the car doesn’t start, but the motorcycle runs fine. There are a few things that could affect both, like if the whole house burns down, but most of the time they are just two separate independent systems. 
As far as improving your Z wave network, it depends very much on the specific devices you have and how far they are physically located from each other.
Start by reading post 11 in the following FAQ, then go up to the top of that topic and read the whole thing and then we can talk more about it. I will link directly to post 11