S is a programming language/environment for statistics and statistical graphics. S-Plus and R are implementations of S. This means that both products are built on the same basis; both execute the same functions (macros). Most common statistical functions progammed for S will run under R and vice-versa.
There are however a number of differences you should be aware of.
Conclusion: Most functions that do not use graphics or basic graphics run in both environments without any problem. Expect however problems when using more complex graphical tools. As this class addresses mainly visual tools, there will be many differences, not so much in what tools are available, but the functions will not be compatible, have different names and different implementations. As a rule these pages are concentrating on R; important differences with S are noted and some documents will be specific for S.