I'll attempt to shed some light on this subject. Essentially time based movement is supposed to keep movement consistant reguardless of actual frame rate. It is essentially based on elapsed time between calls, so that if you have a slow computer the object will appear to move at aproximately the same rate as it does on a fast computer. Let's say you need to move a spaceship from star A to star B, and let's say they're aproximately 50 pixels away from each other. On a slower computer (hypothetical) the spaceship might move 5 pixels per second, on a faster computer it may move 10 pixels per second. At 5 pixels per second 50 pixels would take 10 seconds, at 10 pixels per second 50 pixels would take 5 seconds. But here's the problem, the speed isn't the same, the slow computer takes 10 seconds whereas the faster one takes only 5. So how do you account for that? Time based movement. You call a timing function (usually with millisecond resolution), Save the start time and the end time, and subtract the start time from the end time, to get the actual amount of time elapsed. You then use it to input into your movement. Essentially you adjust the pixels the ship moves per step based on how long it's taken since the last call to get_time. What it results in, is that now, the slow computer will move the ship 10 pixels per second, resulting in the 5 second move, which is exactly what the faster computer does. (Ie the slower ship moves farther in the step than the faster one does). The only major problem with this is that with a really slow computer the frame-rate gets a little jerky, because it apears to jump farther to stay in sync with what a faster computer would do.
Frame based movement of course relies on how fast the computer can update frames. This is why you have some older games that move unplayably fast on more modern computers, and at a correct speed on slower computers. Newer games that use this method essentially rely on the speed the video can update, which means a slow computer on a modern game appears to make the game move "in slow motion" because it can't update fast enough.
So really it's a tradeoff. If you can guarantee at least x amount of frames per second on slower computers, then it shouldn't be a problem, because usually you frame-limit games so they don't go too fast on new computers. (Say 30-60 fps depending on what you're doing). Time based movement on the other hand requires that the computer be fast enough for the game to feel smooth.
I hope this clears up what you're trying to talk about.
Keith