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It is simply and complexly both ...
"Warp. Weft. Woof! are terms from weaving: the threads or yarns that run lengthwise on the loom are called the warp; the crosswise threads or yarns are called the woof or weft. The web is the name given the completed woven fabric, and it also has wide figurative use: What a tangled web* of circumstance you've woven.
All these are Standard." Ref.
*Also known as the care plan!
Original image source:
http://www.wovenwire.co.uk/plainweave.htm
Additional links:
http://www.africancrafts.com/