Slide valves are usually used in compressors designed for process service (air conditioning usually compressing something like ammonia or propane). For air compressors you usually see "turn valves" or "poppet valves". They all do the same thing.
The unloader valve will dump gas back toward suction early in the travel of the gas through the rotors. At that point nearly zero work has been done on the gas and the cost of dumping it is pretty low. At 0% open, no gas is being dumped. At 100% open, maximum gas is being dumped. Depending on the compressor manufacturer, 100% equates to some value between 40% and 70% of full capacity. Each manufacturer sets that number based on their own design considerations.
I'm not aware of any screw compressors set up as two-stage units. Generally that implies intercooling and I've never seen a skid with an intercooler loop. When you need to do more compression ratios than the screw can handle most people set it up so that the screw discharges into another technology (I've seen screws go into 1 and 2-stage recips for years, but I'm starting to see a few go into centrifugal machines).
The unloader valves tend to be more efficient at capacity control than a suction controller or a recycle, but not as efficient as changing the compressor speed.
David