In the world of decorative knotting, there are 2 major schools: sailor's fancywork and Asian knotting. Sailor's fancywork grew out of long ship voyages and an abundance of cordage, and is practiced world-wide. Asian knotting was a basic household skill that evolved into craft and then art, most likely at the hands of imperial court artisans. Much as the cloistered Victorian ladies took up lacemaking with knots (macramé) and developed it to serve a host of new applications, so I imagine court ladies in dynastic China, Japan and Korea proving their skills in embroidery, weaving and silk knotting.
These days, Chinese knotting is all about the knots themselves. The cord tends to be silk-like nylon or rayon, only occasionally real silk. Of course, there were no nylon extruding cord weaving mills in the days of yore. Images of historical artifacts with cord, knots and tassels reveal a cord that is most likely a small woven tube or a fairly straightforward braid.
In Korea, for the living national treasures that hold the knowledge and skills for the cultural art of knotting, knotting (maedup) and braiding (dahoe or tahoe) are inseparable components of one craft.
In Japan, there are several cultural expressions that are often knotted. Braiding (kumihimo) has several schools devoted to that art alone. Gift cards most often bear mizuhiki (paper cords that are usually knotted). Tea bags would be closed by a single but elaborate knot tied in a stiff braided cord. Obis may be supplemented with a braided cord tied with a simple knot. The obi itself is usually tied with an elaborate knot. The furoshiki tradition of wrapping items in simple (if exquisitely embellished) squares of cloth is also a means of transporting items by modifying that square into carrying vessels with simple knots.
Similar to the Japanese furoshiki is the traditional Korean bojagi or pojagi, wrapping cloth. Interestingly, it is the stained glass/pieced jogakbo or chogak po that evolved from peasant traditions of recycling useable scraps of fabric which provides the current classic image of a bojagi instead of embroidered whole cloth as one might find in a royal household.
I have tried to research Chinese wrapping cloths but have either not found the correct key words, or perhaps there are none. Certainly, simple squares of cloth were used to wrap precious objects, food, etc. and tied into bundles to carry objects. But, perhaps, just as in English there is no name for "putting all your worldly treasures in a handkerchief, tying them to a stick and running away" (or is there?!?), there is no formal name or term for wrapping cloths in Chinese.
I asked my dad (OK, a retired mathematician is not exactly the most traditionally/culturally aware specimen to be asking such things, but these are the resources available to me) and he suggested the term "bao fu" (wrap lift/carry).