The digit punches for S-3 and S-4 are the same. The only difference is the date position relative to the bust, with the S-4 being further to the left.
As for rarity, there are no S-4's graded at this level with NGC. NGC has graded/attributed only 11 coins in all grades as an S-4, compared to 319 across all grades for S-3.
Due to the similarities in the varieties, I would guess that there are some S-4s that have been misidentified as an S-3, but even so, the S-4 is much scarcer.