Here's and explanation of the most commonly used wire-cloth weaves.

Plain Weave

Wire cloth in which each warp wire and each fill wire passes over one and under the next adjacent complementary wire in both directions. This is the most commonly used weave.

Plain Dutch Weave

Wire filter cloth the pattern of which is the same in plain weave except that the warp wires are of larger diameter than the fill wires, and are driven up close to each other, resulting in tapered or wedge shaped openings. The warp wires remain in a straight condition and the fill wires take all of the crimps.

Double or Triple Warp

Wire filter cloth which is the same in pattern as either Plain or Dutch Weave except that there are two or three warp wires in place of one.

Twilled Weave

Wire cloth in which each fill wire passes successively over two and under two warp wires and each warp wire passes successively over two and under two fill wires.