A lot of words get tossed around in native gardening projects. It’s worth a moment to clarify.
Naturalized means a plant that is not native, but has been in an area so long that it has found a niche in the environment. Native-gardeners have differing opinions on naturalized plants. Some see every non-indigenous plant as an invader that prevents a native plant from occupying its space. Others focus on the balance of the ecosystem as a whole, and allow for naturalized plants to be an element in it (or at least consider them no more than a minor disturbance that is not worth the bother of eradicating). Queen Anne’s Lace and day lilies are examples of naturalized plants. They were introduced to this continent by European colonists and are part of the average person’s mental landscape of Midwestern wildflowers, but they are not native.
Aggressives are plants that grow out of balance with their environment. There may be some element of the ecosystem that used to keep them in check that has since gone extinct. Trumpet vine and goldenrod are aggressive native plants. They are beautiful indigenous flowers, but they may need human intervention to prevent them from crowding out more diversity of plants. Aggressive plants can be native or non-native, but when the word is used without qualification, it usually means a native plant that spreads rapidly and needs to be controlled.
Invasives are non-native plants that grow out of balance with the environment and crowd out native plants. Invasives are the big bad guys. They reproduce unchecked and destroy diversity. There are introduced species that are not invasive: garden plants that sit neatly where you plant them and do not spread by root or by fruit without a gardener’s deliberate intervention. Hostas are a non-invasive garden plant. An invasive plant grows beyond boundaries and spreads to wild spaces. Most introduced grasses are invasive. Asian honeysuckles are invasives.