what exactly was the Difference, for example, between:
Rapid Fire I, Rapid Fire II and Rapid Fire III
RSP I, RSP II, RSP III
It was only the Global Cooldown, right ? Or are there more other differences?
It's not the cooldown. For MOST powers, the size of the effect itself scales with the level. The II is substantially stronger than the I, and the III is stronger still. There's a bug with Rapid Fire, currently, where all three ranks give the same benefit as the III version (+48%), and a second unrelated bug makes it +68% for many weapons. In the next big patch they'll fix this to 30/40/50% and remove the other bug.
Most powers scale similarly; the II is ~25-33% stronger than the I, and the III is a similar margin above the II, but the exact mechanism might depend on the specific power. For instance, take the High Yield Torpedo skill; it fires extra torpedoes, at a penalty to damage. So if a single torp does 6k damage, then HYT 1 might fire two torps at 5k apiece, HYT 2 fires three at 4k, and HYT 3 fires four at 3k. (Yes, that actually means that the damage dealt by HYT3 is basically the same as HYT2. Go /bug it.)
But for powers like Emergency Power to Shields, it's a very straightforward scaling; EPS2 is just EPS1 but with each number increased by ~25% (size of the shield heal, boost to shield power, etc.) and the exact same cooldown timer.