Etchings and engravings are both methods of creating art with the use of a plate in a printing press. And in both, the plate has grooves that hold the ink.
The difference is in the making of those grooves.
In an etching, the artist typically scratches through a coating applied to the face of the plate. Acid is then applied to the plate. The oil-based coating resists the water-based acid wash. The areas of the plate that are exposed by the artist’s scratches get etched by the acid. In an engraving, though, the artist puts the scratches, grooves, and gouges directly in the plate.
An additional difference is the visual impact of these two methods. The direct engraving of the plate allows the artist to vary the depth and weight of the cut such that the resultant image is substantially three-dimensional.