There are a number of ways to estimate or describe the kinds of plants (and animals) that will grow or are native to an area. For practical reasons, USDA plant hardiness zones are defined by the average minimum temperature. In Athens, Georgia, we are in USDA Zone 7B, with average minimum temperatures of 5-10 deg F. For convenience, the southeastern US is shown below. The United States National Arboretum provides a wealth of detail on plant hardiness zones as well as plants that can be grown.
Much of the southeast US is classified as the Temperature Broadleaf Deciduous Forest ecoregion or biome. The figure below shows the occurence of this biome throughout the world. One might expect plants that grow well in Georgia to grow equally well in Europe, East Asia, and parts of South America, and indeed some of our popular (and unpopular!) non-natives originate there.