Final answer:
Cotton sateen is the fabric with fine crosswise ribs, a lustrous surface, and a highly napped quality, distinct from corduroy, damask, and velvet.
Step-by-step explanation:
The fabric described as a tightly woven lustrous cotton or blend with fine embedded crosswise ribs that resembles poplin but with finer ribs, highly napped, and having an "up and down" quality is known as cotton sateen. This fabric is characterized by its smooth and glossy surface on one side, while the other side remains matte. Sateen is derived from the cotton plant and it differs from satins, which are often made from silk or polyester.
Unlike cotton sateen, damask is known for its reversible patterns, corduroy is noted for its distinctive ridges or "wales," and velvet is characterized by its soft, dense pile. The variety of textiles, including sateen, reflects the historical development and trade of fabric, with materials such as cotton, wool, and silk having deep cultural and economic significance across different time periods and regions.