Okay but in relation to the ST universe then why, if they're bringing two vastly distant points close together, does it take them time to reach those points in certain (or most) instances? Why would they even need a numerical warp scale ("Mr. Crusher, set a course to Romulus, warp 5")? And why do they whoosh off into the distance instead of just winking out like on BSG since, by your own words, there isn't any movement per se?
The whole ST warp model implies movement, a need to get moving very fast (warp speed) in a certain direction to reach the desired destination. And those destinations all take varying times to reach. And, from what I understand the whole warp scale leads up to 9 which is as close to light speed as they can get without actually matching the speed of light.
So, what I'm saying is that in the ST universe they literally move via propulsion (which takes time) verses BSG where they simply jump thru a "door" that leads instantaneously to another point in space. Is this not correct? Edify me here.
Ships in ST have two means of travel. Impulse power, which is regular propulsion that physically moves the ship around, and warp drive.
Theoretical warp drive involves compressing space in front of you and expanding the space behind you. When I say "vastly distant points", I'm talking about millions to billions of kilometers. In ST, Warp I allows the ship to travel 2 million km per second. What that means is the power used to travel at that speed is sufficient to compress and expand 2 million km of space every second. Assuming the average distance between Earth and Mars is about 225 million km, it would take 112 seconds, or 112 compressions and expansions, to get there.
With more power, the drive is capable of compressing even more space, thus achieving shorter travel time. There's going to be some physical limit to this method of travel mainly due to power requirements. Theoretically, though, with infinite power you should be able to compress infinite space but, not being a physicist, I would imagine that would present other problems.
To a stationary observer, the ship would appear to be stretching out into the distance before completely disappearing.
Light travels at 299,793 km per second. Warp I is about 6.6 times faster than light. It doesn't mean the traveler is physically moving through space at faster than light speed, it means the traveler got from A to B in a time shorter than it would have taken light to get there linearly through space.
In Voyager, they destroyed canon by creating this stupid notion that Warp 10 (transwarp) allows the traveler to occupy all points in space at once, thus allowing near-instantaneous travel to any point in the universe. I see two problems with that. First, it was established in "All Good Things" (the TNG finale) that Federation ships in the future were able to travel at Warp 14 and they didn't get anywhere "instantaneously" (neither did the Excelsior, by the way, though, AFAIK, they never established exceeding warp 9.7 as being transwarp). The second problem is that, because of the mechanics of warp drive, occupying all points in space using that technology implies infinite compression of all space, which is a purely stupid notion. The theoretical 4th dimension, or hyperspace, is where one occupies all points in space at once and warp drive has nothing to do with inter-dimensional travel.
ST's warp drive is theoretically possible, according to physicists, given what we know about gravity and its effects on the fabric of space. BSG's dimensional jumps, which is hyperspace just like on Babylon 5 and countless other sci-fi shows that have used that tech, is pure fantasy at the moment as we have no way to know that hyperspace even exists. Wormholes are the closest feasible theoretical thing to instant travel to any point in the universe.