The Plate Tectonics theory states, that the Earths outer shell is divided into several plates that glide over the mantle, the rocky inner layer above the core. The plates act as a strong outer shell compared to the mantle, this shell is called the lithosphere.
The Continental Drift theory states, that part of the Earths crust slowly drifts on a liquid core.
The difference between the two is that continental drift is meaning that the continents were once together to form Pangea, and are slowly moving today. While plate tectonics is showing the structure of the plates and how they are shaped.
The Tectonic Plate Theory can explain why volcanoes occur in certain areas. They also explain how mountains form, and other land masses. For example, the ring of fire is around plate boundaries, and because of that there is a lot of volcanic activity.
Some proof for the Continental Drift theory are fossils. Some animals were indigenous to certain areas and had no way to get to an area, for example some animals were indigenous to Africa but were also found in South America. The animals had no way of crossing an ocean. The continents also seem to fit together, like a puzzle piece. There are also glacial evidence in Africa, meaning that Africa was once south of the equator, and cold enough to have ice. plant fossils were also found in Antarctica. Today Antarctica is very cold and covered in ice. The fossil evidence shows that it was once warm enough to have plants and life.