Native – A good definition of ‘native plant’ is posted on the Lady Bird Johnson Wildflower Center site as a Q&A response. The entire answer is worth a read, but they summarize as follows: “[A native plant is] a plant that occurs naturally in the place where it evolved.”  
The National Arboretum says it this way: “We consider the flora present at the time Europeans arrived in North America as the species native to the eastern United States. Native plants include all kinds of plants from mosses and ferns to wildflowers, shrubs, and trees.” 
The word native should always be used with a geographic qualifier (that is, native to the Southeast [for example]) 
Non-native – Non-native species have been either intentionally or accidentally introduced by humans or their activities. 
An important distinction between non-native species and invasive species is that non-native species do not disrupt the natural functions and processes of our native ecosystems. In other words, non-native species do not cause environmental harm. 
There’s a big difference between ‘non-native’ and ‘invasive’. In fact, when many non-native plants are introduced to new places, they cannot reproduce or spread readily without continued human help (for example, many ornamental plants). 
Responsible plant breeders have worked diligently for decades to bring us well-behaved plants from all over the world. Reputable magazines, like Fine Gardening, will tell you if a plant is a problem here.
For example, while natives would be better, these non-natives pose no threat to us here in Peachtree Park (they may be problematic in other parts of the country):
- Evergreen Azalea
- Lenten Roses
- Japanese Maple
- Non-native Columbine
An additional caution from the Extension Service at UGA: “Beware of ‘Meadows in a Can’ or other wildflower seed mixes that are formulated for other regions of the country, such as the Pacific Northwest or the Northeast. Many of these mixes contain non-native species as well as species not well suited for the heat and humidity of the Southeast. For best results, look for seed mixes formulated for the Southeast.” 
Exotic – A plant not native to the continent on which it is now found (Plants from Europe are exotic in North America; plants from North America are exotic in Japan). 
Invasive – A plant that is both non-native and able to establish on many sites, grow quickly, and spread to the point of disrupting plant communities or ecosystems. 
From the Presidential Executive Order 13112 (February 1999): ‘An invasive species is defined as a species that is 1) non-native (or alien) to the ecosystem under consideration and 2) whose introduction causes or is likely to cause economic or environmental harm or harm to human health.’ 
The Georgia Exotic Pest Plant Council (GA-EPPC) has a list of invasive species and categorizes them as: 
- Category 1 – “[An] exotic plant that is a serious problem in Georgia natural areas by extensively invading native plant communities and displacing native species.” There is also a Category 1 Alert which is “[An] exotic plant that is a not yet a serious problem in Georgia natural areas, but that has significant potential to become a serious problem”.
- Some Category 1 invasives in Peachtree Park:
- Chinese Privet
- English Ivy
- Asian Wisteria
- Category 2 – “[An] exotic plant that is a moderate problem in Georgia… but to a lesser degree than [a] category 1 species.
- Some Category 2 invasives in Peachtree Park:
- Bermuda Grass
- Japanese Privet
- Amur Honeysuckle
- Category 3 – “[An] exotic plant that is a minor problem in Georgia natural areas, or is not yet known to be a problem in Georgia but is known to be a problem in adjacent states.”
- Some Category 3 invasives in Peachtree Park:
- Callery Pear (Bradford pear)
- Queen Anne’s Lace
- White Mulberry
- Category 4 – “[An] exotic plant that is naturalized in Georgia but generally does not pose a problem in Georgia natural areas….”
- Some Category 4 invasives in Peachtree Park:
- Chinese Parasoltree
- Chinese Holly
- Japanese Holly
- Red, Tall and Small-flower Morning-glory
- Cherokee Rose (that’s right – the State flower of Georgia)
Naturalized – A non-native plant that does not need human help to reproduce and maintain itself over time in an area where it is not native. Invasives are a small, but troublesome, sub-category of naturalized plants. 
Aggressive – Thuggish is a commonly used term. The Chicago Botanic Garden says this: “An aggressive plant is one that spreads faster than preferred, or into an area of your garden where it is unwanted. A plant may be aggressive in one area of a garden or neighborhood and well behaved in another.”
Not all aggressive plants are non-native.
Weed – “A weed is simply a plant out of place.” – Ryan Gainey.  We have some well-behaved weeds, such as the Daisy Fleabane, that come back every year and flower. They are attractive, the pollinators love them and so do we. The weeds that we have are known to us and are fairly well-behaved.
This is different from a ‘noxious weed’, which is a plant weed that is particularly troublesome and are banned by law in many states.  Be careful not to take home a noxious weed and plant it since some are very aggressive and you will have trouble containing or eradicating it.
Endangered and Protected – There’s a list of plants that are protected in Georgia by the provisions of the Georgia Wildflower Preservation Act of 1973. 
Illegal Harvesting – “Transplanting wildflowers from their native habitats to cultivated landscapes is discouraged. It is prohibited if the plants are rare or endangered, or if they are located on land owned by the state or federal government. It also is illegal to collect plants from private land without permission from the landowner.” 
Plant Rescue – “Some organizations, such as the Georgia Plant Conservation Alliance, the Georgia Native Plant Society and the Nature Conservancy, conduct organized rescues of native plants that are threatened by construction, provided permission is given by the landowner.” 
References and Additional Information
 Doug Tallamy: Bringing Nature Home – Gardening For Life
 Lady Bird Johnson Wildflower Center: Question – what is a native plant?
 Wasowski, Andy. “Provenance, defining our terms.(native plants).” The American Gardener 77.6 (Nov-Dec 1998): NA.
 The United States National Arboretum: What is a Native Plant Anyway?
 USDA Natural Resources Conservation Service – Connecticut: Native, Invasive and Other Plant-related Definitions
 Georgia Exotic Pest Plant Council (GA-EPPC): List of Non-native Invasive Plants in Georgia
 Vital Signs – Maine: What Is An Invasive Species?
 Attributed to Ryan Gainey, Atlanta gardener, poet and raconteur
 Georgia DNR – Natural Resources Division – Rare Plant Species Profiles; see also Protected Plants of Georgia (outdated 1995 document) for helpful links
 Native Plants for Georgia Part III: Wildflowers (B 987-3) – Obtaining Plants and Learning about Native Wildflowers
 Georgia Plant Conservation Alliance
 Georgia Native Plant Society
 Nature Conservancy – Georgia
 The Native Plant Society of Northeastern Ohio – The Importance of Native Plants
 The Intown Hawk: Natives as Alternatives