A Samsung 20R cell and a Samsung 25R cell are both the same size (18mm diameter, 65mm long). One is a 2Ah cell, the other is a 2.5Ah cell. They are both approx 4V fully charged. Connect 5 20R in series and you have an 18V 2Ah battery pack. Connect 2 of those in parallel and you have a 4Ah 18V pack. Do the same with the 25R and you have a 5AH 18V pack.
The same holds true for LG HD2 and LG HE2 respectively.
(can't say for certain about the torn down packs mentioned, but the steel could also have been for thermal transfer. Other packs may well do the same using thermally conductive paste.)