Damask
You are probably thinking of the fabric used for table linen called Damask. It is a special weave that forms a pattern in the cloth. See the link to the article I have provided.
linen
Linen
A fine white linen manufactured in Flanders is known as "Holland cloth." It is a high-quality linen fabric traditionally produced in the region and favored for its softness and durability. Holland cloth is often used for garments, table linens, and household items.
Linen in table appointments refers to the fabric items used for dining, such as tablecloths, napkins, and placemats. Typically made from natural fibers like cotton or flax, linen adds elegance and texture to a dining setting. It not only enhances the aesthetic appeal but also provides functionality by protecting the table surface and offering a comfortable dining experience. Linen can come in various colors, patterns, and weaves, allowing for versatile styling options.
Gauze
Linen fabric was used, and they got it from the flax plant, which they weaved into fabric. It was combed and spun with a balance wheel on a spindle for spinning the thread from flax. The types of linen produced ranged from a course sackcloth type of material to the finest, almost transparent linen.
Cambric
Linen is made from the fibers of flax plants.
Linen, mud, onions, and reeds were placed between the eyeballs and eyelids as false eyes or in the nostrils.
The types of fabric used in the 1960's is linen
Table covers can be linen or spandex. Linen table covers can be of any cloth material including silk, polyester etc. Spandex material is one of the largest used materials for table covers these days.