While both marquetry and parquetry can beautifully decorate fine furniture, to better understand the differences, let's quickly review.
Marquetry: "marquetry" is inlays of different color woods (or other material) and it typically depicts some form of flowers or objects, imagery or scenery, and can be small patterns or motifs. Some typical examples are inlaid eagles on fine American furniture, graduated bell flowers down the legs of a fine English table, or floral garlands across the side of a tables frieze.
Parquetry: "parquetry" is similar in that it is inlays of varying colors of wood, however, parquetry is typically geometric designs or patterns. Commonly seen today on flooring, parquet floor resemble the delicate inlays of 18th and 19th-century French furniture.