No.They are not the same.
Epidermal cells and cork cells are two types of cells found in the outermost layer of plants. They occur in different parts of the plant body at different stages. The main difference between epidermal cells and cork cells is that epidermal cells cover the entire plant body during primary growth whereas cork cells cover the stem and root of the plant after the secondary growth of the plant. Epidermal cells are found in leaves and other immature parts of the plant. They occur as a single layer of cells. Cork cells originate from the cork cambium.