I haven't seen any official terms for this method and as far as I can tell, it isn't a historical practice with trichinopoly. For the sake of describing them, however, I'm referring to two methods of using multiple wires as "simultaneous" double wire and "alternating" double wire.
Simultaneous double wire refers to treating two wires as if they are one wire. Where one wire goes so does the other; both go through each loop in the knit. Simultaneous wire doubling creates a denser knit that is kind of like double knit, although distinct in its own way. The impact of this construction method is visually apparent regardless of whether or not different colored wires are used - although multiple colors does make it more obvious.
Alternating wires are offset such that one wire is the "row" below the first, and they spiral their way down the piece. This has no impact on the weave density, nor the weave pattern or shape - but if multiple colors are used, it can create a "banding" effect as the colors alternate in rows down the piece.
With either method, I intentionally offset the length of the two wires so that when I have to splice new lengths onto either wire, I don't have two splices in the same spot. Splices can already cause weave congestion if they're not placed well or correctly, and having two of them tends to just lead to difficulties weaving around it, possibly even defects in the finished piece.
I will also note that it's possible to use more than two wires, either alternating or simultaneously. If alternating, the result is the possibility of additional color bands, which can be a great aesthetic choice. I've tried up to 3 myself, though I suspect at a certain point it will become confusing where to start each wire relative to the others. I wouldn't necessarily recommend more than two wires be run simultaneously, as though I haven't tried it myself yet, two wires already significantly increases weave congestion and adding more will probably slow your knitting speed to a painful crawl.
26/28 gauge | 5 ribs | 8mm tool | 5mm draw
Single knit double wire simultaneous
Compared to the alternating wire version to the right, this particular piece demonstrates the mixed color and knit aesthetic changes of a simultaneous double wire weave. The green and peridot weren't always kept in the same arrangement relative to each other on each loop, which gives the piece an irregular yet interesting coloration. Hypothetically, it should be possible to create a regular pattern from the colors by keeping the same wire orientation on each loop - but in practice, this would certainly be tedious.
26 gauge | 5 ribs | 8mm tool | 5mm draw
Single knit double wire alternating
Compared to the simultaneous wire wire version to the left, this piece demonstrates the alternating rows of knits over the length of the chain. The result is a banding coloration pattern, but a weave that's exactly the same density and loop shape as any other "single wire" piece would be for this combination of gauge, ribs, tool size, and draw diameter.
28 gauge | 5 ribs | 8mm tool | 4mm draw
Single knit double wire simultaneous
This double wire piece uses similar a dark "smokey quartz" colored wire along with a brighter color closer to natural copper, both in the relatively thin 28 gauge, to create what from more than a foot or so away looks like a worn and tarnished metal chain. In some of the closeup pictures it's quite apparent there are two separate wires, but this level of detail is difficult to perceive unless closely examining the chain, so most of the time, using these two similar colors that are both metallic creates a blended and textured effect, rather than having two disparate colors. Using two wires also increased the weave density enough that the thinner wire was reasonably strong even in what would otherwise have been a fairly loose and open weave.