Are the plate boundaries the same as the edges of continents?

No. Not all plate boundaries are at the edges of continents, nor do all edges of continents correspond with plate boundaries. Many plate boundaries are found in the middle of oceans, while the continent of Africa is being torn apart by a developing plate boundary. Some edges of continents, such as the west coast of South America are near plate boundaries. These are called active continental margins. Others, such as the east coast of North America, are nowhere near plate boundaries. These are called passive continental margins.