Embossing on paper or other materials is the process of producing sunken or raised designs, or reliefs. Embossed images or designs can be felt because they are on a different level than the surrounding area, and are three-dimensional.
Engraving on paper or other materials is the process of incising images, a design, or words onto a hard, flat surface by cutting or shaving grooves into it. Engraved designs are carved into the surrounding area.
Embossing molds existing materials into their designs without removing any, while engraving actually carves out and removes the material into which it is being carved.