(There's a couple of these questions kicking around, but I didn't see anyone give the "two boosted copies" answer. Generically, I'd say that's the right answer, since it gives an actual causality violation.)
In your scenario, the two planets remain a hundred thousand light years apart. The fact is, you won't get any actual causality violations with FTL that way. The trouble comes if the two planets are moving away from each other. So, let's say that your warp drive travels at ten times the speed of light. Except if the two endpoints of the trip are moving, then what does that mean? Ten times the speed of light relative to which end?
Let's say Tralfamadore is moving at a steady 20% of $c$ (the speed of light), away from Earth. (So, Earth is moving at a steady 20% of $c$ away from Tralfamadore.)
If I leave Tralfamadore (in the direction of Earth) and I am travelling at anything less than 20% of $c$ relative to Tralfamadore, then I am still moving away from Earth. I'll never get home.
Let's say instead I am travelling at 60% of $c$ relative to Tralfamadore. I will catch up to Earth. Relative to Earth, how fast am I approaching? You might guess the answer is 40% of $c$, but it's 45.45%.
Generally, the velocity subtraction formula of relativity is: $$w = (u-v)/(1-uv/c^2)$$
Let's say instead I am travelling at 100% of $c$ relative to Tralfamadore. Plug $u=c, v=0.2c$ into the formula and get $w=c$. Relative to Earth, I am approaching at 100% of $c$! The speed of light is the same for everyone.
So finally, let's say instead I am using your warp drive to travel at 1000% of $c$ relative to Tralfamadore. Relative to Earth, I am approaching at -980% of $c$. In Earth's reference frame, I will arrive on Earth before I leave Tralfamadore. Now you may say this in itself isn't a causality violation, because we've applied Earth's calendar to Tralfamadore. And that's true, but I'll make a round trip:
- In the futuristic Earth year of 3000, Tralfamadore is 98,000 light years away, and receding at 20% of $c$. I leave Earth at 1000% of $c$, relative to Earth.
- In Earth year 13000 Tralfamadore is 100,000 light years away, and I catch up to it. I turn around and leave Tralfamadore at 1000% of $c$, relative to Tralfamadore.
- In Earth year 2796, I arrive home.
Earth's calendar certainly applies to Earth, and I arrived home two centuries before I left. No two ways about it, I'm a time traveller!
There is nothing special about ten times the speed of light. Given a warp drive that moves a certain amount faster than light, you can make the above time machine using two endpoints that are moving apart a certain amount slower than light, provided that the warp drive can move faster than light relative to either end. This time machine works for any form of FTL: tachyons, warp drives, wormholes, what have you.
Ok, so let's say you had a wormhole. How long would it take to get from point A to point B using it? Let's say it's instantaneous. A traveller would arrive the same moment they left, spend some time at point B (it's really a nice place; the B-ian people are friendly and the food is great), then use the wormhole to go back to point A. No problem right? No violation of causality? Perhaps, but you need to ask yourself "when is right now at point B?" Consider this diagram:
This is a Minkowski diagram. The red axes represent the reference frame we're in and the green axes represent a reference frame at some high velocity relative to ours. So now ask yourself that question, when is right now? By the red frame, right now is the x-axis. The wormhole could take you to any point along it. But what if I enter the wormhole travelling fast enough to be in the green frame? In that frame, instantaneous travel is anything along the x'-axis. Notice that accordingly, that would put me into the red frame's future (we're just looking at the first quadrant). So you say "well that's simple, the wormhole isn't moving in my frame so it would make use of my definition of instantaneous". Here's the bigger problem. Now if I'm in the green frame and enter the wormhole, I travel along the x-axis and the point I end up is actually in my past (trace a line from somewhere on the x-axis back to the ct'-axis that is parallel to the x'-axis, it leads to the past).
How does this explain how I can send a message back to 2004? Say I have the wormhole, I enter it in the red frame (let's assume that's the Earth frame). Then I get to point B, accelerate to be in the green frame and go back through the wormhole to our point A at x=0. So let's run through this. I start at x=0, I used the wormhole to travel to some point on the x-axis, I speed up (so shift the green frame so that the green origin is on the x-axis at our chosen point), then I return through the wormhole to x=0 except remember I'm travelling along the x'-axis now. Voila, I'm in 2004.
But hold on, you say. Didn't I already establish that the wormhole uses the definition of instantaneous from its own frame; the red one? True, I did say that. But what if at point B I find another wormhole travelling in the green frame that links back to x=0? Or what if I found a way of speeding up the other end of the wormhole? Then I could certainly travel back to 2004.
The only way to prevent me from using a wormhole to travel to the past is to make all wormholes exist in the same reference frame and transport objects using that frame's definition of instantaneous. But that would mean there is a preferred reference frame in the universe. And that would be a matter for another question on this site.
Best Answer
The difference is that in the case of wormholes, it is not certain that closed timelike curves (and thus violations of causality) actually occur, and if they occur, in which form. There are different approaches to the issue, for an interesting read (which also treats other kinds of spacetimes that potentially violate causality), see this. The general idea is that causality violations might be suppressed by quantum effects.