There are 3 categories within the 'aggressive/invasive' plant designation.
Invasive exotic - non-native species that displaces native species in otherwise natural environments
Kudzu, Wisteria, Ailanthus, Sapium
Aggressive - grows like mad and needs lots of monitoring to keep under control, mostly vines and large shrubs in gardens
Cup-of-Gold vine, Bougainvillea, creeping bamboos
Garden invasive - mostly perennials that spread underground or annuals that reseed everywhere
California Poppy, Alyssum, Yarrow, Mexican Evening-primrose
Exotic invasives are location dependent. Japanese Honeysuckle is invasive in the East but not here, it's just aggressive. Same with Wisteria, Sapium, Vinca, privet.