Difference between single output rail psu-s and dual rail ones

Oh boy, this is a tough question to answer concisely, mainly because PSU manufacturers have taken so many liberties with the definition of 'rail'.

In general, each rail is a set of combined outputs that are tied to a common OCP (Over Current Protection). Prior to version 2.3, the ATX specification requires that any single output wire carry no more than 240VA (240 DC watts for our purposes). At 12 volts DC, this translates into 20 amperes on any single wire. Thus, most PSU manufacturers that use multi-rail 12 volt outputs will bunch outputs into 18 to 20 ampere rails.

This does not mean that the rails actually come from separate DC converters (some PSUs use multiple 12 volt supplies each with their own OCP, but some use a single 12 volt supply with multiple OCP. The latter form is called a 'virtual rail'), just that there's more than one OCP mechanism serving 12 volt outputs.

Since the 12 volt outputs are protected by multiple OCP mechanisms, there is now a need to distribute the 12 volt loads such that the OCP mechanism doesn't trip.

For example, a single AMD Radeon HD 7990 has a TDP of 375 watts. 75 watts can be drawn from the socket which means that 300 watts need to be drawn from the auxiliary PCIe adapters. The 300 watts will be provided by 2 x 8-pin auxiliary PCIe connectors rated at 150 watts each (6-pin are rated at 75 watts each). Each of the 8 pin connectors will deliver approximately 12.5 amperes (150 watts / 12 volts). If they were both connected to a single rail which was capped at 20 amperes per the pre-ATX 2.3 specification the combined output of 25 amperes would cause the OCP to trip on that rail. Thus, PCIe 8 pin connectors are often on a rail that's shared only with a PCIe 6 pin connector for a combined 225 watts, which is just under the 240 allowed per the specification.

12 volt power to the motherboard, CPU, SATA, and MOLEX is usually provided on one rail, with 12 volt power to PCIe peripherals on subsequent rails.

If that sounds a bit complicated, you'll be happy to know that most people and most PSU manufacturers agree with you. The mandatory OCP was removed in ATX 2.3 (although it remains recommended) and many PSU manufactures have reverted to single-rail designs which require no such balancing act.

I hope that answered your question.