I have been told that both of these use the same R&P and same gears. Is this true?
Same R&P teeth, yes. Not the same 1st-5th gears. Albins does have slightly wider gears than an S5D, but not by much.
how does the Albins achieve a higher rating than the S5D?
Albins uses a Torsen differential (12 planetary gears, 6 each driving a sun gear), which is far stronger than the 4-spider open diff in the S4D/S5D. Also adds some traction biasing effect (limited slip diff) to get power to both wheels under acceleration.
There are some other design features with the housings and the way the bearings and gears are done in the Albins to give it a stronger overall rating.
If second gear is the weaker link in an S5D what does Albins do differently to overcome this?
2nd gear is cut onto the mainshaft with 1st gear (like a VW), rather than being splined onto the shaft. The S5D has a splined 2nd gear, and the way the gear is offset to the splines, it creates a bit of a weak spot.
There are many other small factors that add up to an Albins having an overall higher capability to an S4D/S5D. I have been pushing the S4D/S5D lately because I know that most people don't use all of the power they actually have other than a few short bursts from time to time. I truly believe the Weddle is the best "bang for your buck" if you have a limited budget.