Coaxial and triaxial cables are two variations of electrical cables designed to shield the conductors from electromagnetic radiation. If you're familiar with other types of twisted pair cables, coaxial cables are similar to these. The main difference is in how the cable cores are made.
Coaxial cable (coax) consists of two conductors which share the same axis. To separate them electrically, at least one must be cylindrical and larger in diameter than the other. Coaxial cables are inherently unbalanced, which may be bad news concerning immunity to EMI (electromagnetic interference), but this is often overcome by their efficiency in connecting to high-frequency antennas. The choice of coax is ordinarily dictated by the antenna design itself.
In referring, above, to “at least one must be cylindrical,” this acknowledges the use of a hollow center conductor which is used in some large cables to take advantage of the skin effect (at high frequencies) in which nearly all the signal is confined to the outside of the conductor. The core material can be eliminated with little effect on performance, and this can result in reduced weight or cost.
Interestingly, there are specially designed coaxial cables which, themselves, function as antennas. They are constructed with a slit or perforated shield, which ordinarily would be a poor design, but leak enough signal to/from the center conductor that they radiate over their entire length. These are used, for example, in subway tunnels to provide RF access to those systems operating underground.
There are many coax cable designs & types, including those with sophisticated, highly-effective multiple shields, and many different cable diameters with corresponding higher losses in smaller [center conductor] gauges and low loss in the larger gauges. And there are many differences in insulation materials that affect safety, flexibility, and signal handling. Technology is constantly changing.
Multiple shields in coax are normally “unitized,” that is, electrically connected to one another.
Triax cable is similar to coaxial cable in that all the conductors share the same axis. However, three conductors are used in triaxial cable -- at least two of which must be cylindrical and insulated from one another.
Triax cable can be used in many coax applications, but it offers an additional shield as well--not just another layer of shielding. The outer shield covers the coaxial cable inside, providing extra protection against electromagnetic interference (EMI).
Quadrax is a four-conductor cable. The two separate shields share the same axis, but the two remaining conductors are a twisted pair. Like Triax, the shields are insulated from one another, which helps improve noise immunity.
It is also well suited to confining noisy signals, such as pulses, from interfering with other low-level circuits. This explains its application in radar display buses.
Its greatest usefulness is below 50 MHz.
Twinax also has two twisted conductors, but they are surrounded by a single (or double, but not isolated) shield. Twinax almost completely violates the common-axis idea — unless you consider the “pseudo”-axis of the twisted pair. (Historically, the name was devised to imply a “next generation” of coax, primarily in data communications applications, though Twinax is no longer a preferred medium for new applications in this market.)
There are many variations within all the “-axial” designs, but a basic understanding of their family names may help in making sensible application decisions, or at least better appreciating the decisions made by avionics and airframe engineers.