2 sorts of output drivers:
1) Constant Current (CC)
2) Constant Voltage (CV)
Although the do exactly the same thing, they control a load, using either a linear pass transistor (smooth but lossey) or a switch mode inductor (efficient but noisey), the effective control term is different.
The CC driver will apply an output voltage to the load until it reaches either the maximum voltage it is possible of supplying or until it's output current meets the target current.
The CV driver simply outputs a target voltage and the current is controlled by the loads impedance (resistance for DC)
The reason we use CC drivers for LED's is that they have a very non linear impedance with voltage characteristic. Below some threshold voltage they are virtually non conductive (uA only flow), then suddenly they start to conduct (and emit light) and over a few tenths of volts there current demand rockets. The threshold voltages at which the characteristic changes depends upon the makeup of the LED (colour, junction type etc) but also on temperature. So if you used a CV driver, small changes in LED impedance would cause massive changes in the current being driven through the LED, generally resulting in it failing (via overheating). Using a CC driver results in a controlled current flow at all times, pretty much irrespective of the output voltage, and for an LED current = light output broadly speaking.
Various types of driver exist, with most modern ones being switch mode drivers, that store a tiny amount of charge in the magnetic field of a small inductor, and use this to transfer a flow of current between two differential voltages. They oscilate at very high frequency (typically 200KHz) and charge / discharge the inductor to force the current to flow. Depending on the architecture of the particular driver it may be able to either just reduce voltage (buck converter, i.e. Vout < Vin always), increase voltage (boost converter Vout > Vin always) or both (Buck/Boost Vout>Vin>0).
Which type of Switch mode driver you choose depends on the potential of your supply voltage and the maximum load voltage. Typically, for LED's the output voltage is going to be less than the maximum voltage that the datasheet says you can apply to the led without damage. Where you have a choice, you would normally pick an input voltage that is higher (by some margin) that this maximum output voltage requirment, therefore you can use a simple Buck convertor. if you are designing a system for maximum efficiency, it all gets a lot harder because the efficency of the convertor is not linear with deltaV.
Hope that helps!