Fly tying thread has a simple job - hold your chosen materials to the hook.
It gets more confusing after that though due to the wide variety of sizes, colors, and materials.
Size is a constant source of confusion. Just remember that 3/0 is bigger/heavier then 6/0 (making 18/0 quite tiny). For thread measured by "denier", 210D is bigger/heavier than 140D.
For more variation, gel spun diameter is different from a polyester or nylon thread. In other words 3/0 gel spun isn't the same as 3/0 polyester or nylon.
For stretch, nylon has about 25% stretch, polyester around 15% stretch, and gel spun only 3% stretch.