Drapes are often made with heavy fabrics, are lined (often with a heavier fabric to black out light), and run from the top of the window to the floor. The usually have pleats at the top – thereby giving them their draping effect. Drapes can even “puddle” on the bottom on the floor! Drapes are usually made to order.
Curtains are often unlined and fit to the window size. They are made from a variety of fabrics, weights of fabrics and a variety of colors and are less formal than drapes. Curtains are also made to GO OVER blinds or shades. Curtains can be bought in predesignated sizes.
In terms of blocking cold or heat … a lined drape could work as could a curtain over a blind or shade. Choose what works for your situation.