Is warp 10 the same speed as trans-warp? Does it means infinity speed in both cases?
In Threshold episode Tom Paris is experimenting with warp 10 speed and the effects of this are quite poor. Accelerated form of natural human evolution, two hearts etc.
In the same time, Borg drones created out of humans, does not have any negative (or any at all) effect of traveling with trans-warp speeds. How can this happen?
Answer
It's definitely important to note that Threshold is really bad.
Having said that, Warp 10 and transwarp are not the same term, but they aren't unrelated either. Warp and transwarp are different ways of measuring a ship's velocity relative to the outside world (since a ship in a warp bubble is theoretically stationary, it just warps the space around it to actually break the light barrier, insert technobabble as you see fit).
Think of it like this -- the sound barrier, right? If something is traveling at subsonic speeds, it's fair to measure its speed in MPH or KPH or whatever the preferred metric is. Upon breaking the sound barrier and attaining velocities several times the speed of sound, one measures their speed as a factor of Mach; Mach 2, 3, 4 and so on. It becomes a bit cumbersome to think of the speed in terms of MPH or KPH and ultimately less useful under most circumstances, in particular if the craft is regularly traveling several times faster than sound.
The light barrier is another such breakpoint in terms of measuring speed; one would not clock a ship which is travelling roughly 11c as Mach 9593023; better to just call it "Warp 2"!
In Star Trek, the light barrier has been smashed and now uses the idea of Warp 10 as being unattainable, citing it as being 'infinitely fast'. Whether or not that is literally the case, or an artifact of their perception due to their inability to actually get there (barring Threshold, aiee) could be speculated on; however, Star Trek does lend us the ill-explored idea of transwarp, which is touted as significantly faster than plain old vanilla warp. It is simply another scale for measuring the speed of a ship moving at superluminal speeds.
The original Excelsior experiment having famously failed in Star Trek III, the assumption has been that they simply abandoned the project and instead moved on to making their own warp drives more efficient; indeed, whereas old warp speed can be commonly calculated as lightspeed times the warp factor to the power of 3 (Warp 2 = 8c, Warp 3 =27c, and so on), the TNG warp scale is lightspeed times the warp factor to the power of 10/3 (3.333...), which means that Warp 2 is something like 11c, Warp 3 is about 29c, and so on. The math breaks during the transition from Warp 9 (1516.3c) to Warp 10(apparently infinite) and so the speed starts to climb towards infinity, which is why it is A Big Deal when the Enterprise-D, the Borg, and other vessels are capable of pushing Warp 9.5 and higher - even fractions of warp speeds at that point are significantly faster than the previous increments.
Speaking somewhat non-canonically; the TNG Technical Manual hints at the idea that warp factors exist because there are certain warp fields which are more or less "easier" to maintain; it's more energy efficient to travel right at Warp 3 than Warp 2.9, which is why these seemingly arbitrary Warp speeds exist at all. What transwarp would offer, then, is a completely new scale that would be to warp speed what lightspeed is to Mach, and Mach to MPH, etc.
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