While some use the terms "exotic" and "invasive" interchangeably, I think in general there's a distinction to make. For example, in the Netherlands the Japanese knotweed completely dominates everywhere it grows, choking the far more biodiverse native vegetation. As it threatens biodiversity among other things it is invasive. However, the Black swan is also a non-native species that lives and breeds in the Netherlands in low numbers (around 70 pairs if I'm not mistaken). While it may compete to some extent with our native swans, it's biology and low density make it a reasonably "harmless" exotic.
Of course, an exotic can turn invasive, but it doesn't have too. Invasives are also not necessarily exotic, as native species can turn invasive too (Molinia cearulea, Purple moor-grass, comes to mind, but I'm sure there are better examples).