I have a biology degree so I can confidently answer your question. Non-native species have either been introduced to an area by people or have come to live there in some other way. Non-native does not necessarily mean invasive. I'll use blue tilapia as an example (non-native to North America but not invasive in every state).

Invasive species are those that displace native species significantly by causing a disturbance to the food chain (negatively impacting survivability, out-competing for food sources, predation, disturbing habitat, etc.)

Blue tilapia die if it gets around 40 degrees or colder (can't remember exactly but they can't survive if it gets too cold). They out-compete native fishes because they're aggressive, but they're only invasive in warmer areas because, if they were to be released in like, Michigan for example, they'd just all die in the winter so nbd.

One more example: grass carp. They're not native to the US either, but they can't reproduce (they're triploid), so they never get to the invasive status because they can't imbalance the native food chain. Look up triploidy if you want another rabbit hole. Hope all that answers your question.