I thought the S stood for standard as opposed the the deluxe features of the bound 4001, but according to Paul Boyer on another forum:
By all official accounts, S stood for "special" in that they were originally made "special" for a large export order to Rose-Morris in England for sales in Europe. RM chose a lower trim package, presumably to result in a lower sale price and to satisfy European taste. Rose-Morris gave them their own model number: RM1999. Eventually, the S model was offered for sale in North America, first as the 4001S. In the last years (to be determined), the 4001S and the single-pickup 4000 shared the same "chassis" - a set neck glued to a one- or two-piece body; no neck through. The 4001S and 4000 went away in the mid 1980s, and for a while, the 4003S was made with many interesting permutations, such as the 4003S5 five-string, the 4003S8 eight-string, and the sought after 4003SPC models called the Tuxedo (White), Redneck (Red), and Blackstar (Jetglo), each with painted maple fretboards with tiny microdot position markers.