There are distinctions between non-native species and invasive species. It’s not a hard-and-fast line to draw, and VERY context dependent. But not everything non-native is, in fact, invasive.
Non-native species can live within an environment they didn’t evolve in, but there are enough limiting factors that they don’t take over. Just about every common garden annual is non-native, but I plant zinnias and sunflowers like everyone else. They’re cheap, easy to grow and collect seed from, bloom a long time, and attract pollinators a large chunk of the season while native species are more sporadic. Dandelions are another example where I live. Like many of our native species they are deep-rooted perennials that hold onto soil, and take the place of the earliest spring prairie blooms that are no longer there to support pollinators especially in developed areas. Most of the time, they can live alongside native species, but we may remove them if we have specific concerns.
Invasive species take over an environment, pushing out other species. They spread aggressively or breed quickly, can live in a broad range of environments, and are often not favored as food by native species or cause major damage to the populations of native species. In their native environment, there is something to keep them in check- predators, insect pests, diseases, hard winters, something that the species co-evolved with. In an environment without those limiting factors, their populations explode to the extent that they damage the environment. Water hyacinth is a huge problem because it grows so fast it literally clogs waterways, changes the flow pattern of rivers, and makes waterways unlivable for some native species. We aggressively pull all the garlic mustard we can because if we don’t, we will end up with a forest understory full of only garlic mustard and no other plants.