Final answer:
The Appalachian Mountains are older with a history of tectonic collisions and have eroded rolling hills, while the Teton Range is younger with rugged peaks from the Laramide Orogeny. Both ranges, however, were formed by tectonic forces and have undergone significant erosion.
Step-by-step explanation:
The Appalachian Mountains and the Teton Range, part of the Rocky Mountains, differ mainly in their age and formation processes. The Appalachians were formed over a period starting in the Paleozoic, with collisions of island chains and continental masses during the formation of Pangaea. This region now consists of eroded hills and valleys, indicating its great age. In contrast, the main growth of the Teton Range took place during the Laramide Orogeny in the Late Mesozoic and Early Cenozoic, a much more recent event geologically speaking. This range is characterized by dramatic, rugged peaks, indicative of its younger status.
However, both mountain ranges have similarities in that they were both formed through tectonic forces and have experienced significant erosion. Their landscapes provide important geological insights into the Earth's history and are home to diverse ecosystems and biotic communities.