Caimlas,
Technically, to be a two stage trigger, both stages involve unloading the sear. What you describe is called 'slack' and is just a loose trigger. A Mauser K96 has a two stage trigger. If you look at the trigger, you will notice a 'lump' that changes the mechanical advantage so that the first part of take-up - the first stage - moves the trigger into a position close to disengage over a long, but relatively light pull. Once the leverage changes, the final pull has less leverage, but shorter travel.
As an analogy, imagine that we want to protect our castle by putting a boulder up on the hill overlooking the road in. We don't really want it right on the edge of the cliff, because then it might fall accidentally. So we put it back from the edge. But we need to get it right up to the edge if it looks like we might need it, so that with only a little effort is needed to push it over. So we keep a big lever near the boulder. In an emergency, the lever is used to ge the boulder into 'firing position' (first stage) so that with just a small push, the bould can be forced over the cliff (second stage).
I'm not sure if the above analogy works, but basically, you will always have a certain load on the sear. In the case of the above Mauser K98, you have to hold back the force of the striker. And you must do it with enough sear engagement that you can't accidentaly but the sear off. Let's say that this requires 12 pounds of total force. Utilizing levers, we can either spread that force over a long distance - a light long pull, or use a shorter distance and a heavier pull. The less movement of the trigger, typically the less change to effect aim. But a short pull would be a heavy one.
Or, if you are really clever, you divide the pull into two stages. In the first stage, you have a long pull that eliminated say 9 of the 12 pounds. At this point the leverage changes so you have less mechanical advantage. But you only have 3 pounds to overcome, so even thoug you have much less leverage (and thus les trigger movement) the total force requires is much less. A 12 pound trigger has become a 9 pounds plus 3 pounds, with the first part spread over a lot of movement, and the crtical last few pounds is short and crisp
Clear as mud?