Technically, SML’97 as defined in the Definition requires only a minimal initial basis, which, while including the types int, real, char, and string, need have no operations on those base types. Hence, the only observable output of an SML’97 program is termination or raising an exception. Most SML compilers should agree there, to the degree each agrees with the Definition. See UnresolvedBugs for MLton’s very few corner cases.
Realistically, a program needs to make use of the Basis Library. Within the Basis Library, there are numerous places where the behavior is implementation dependent. For a trivial example:
val _ = valOf (Int.maxInt)
may either raise the Option exception (if Int.maxInt == NONE) or may terminate normally. The default Int/Real/Word sizes are the biggest implementation dependent aspect; so, one implementation may raise Overflow while another can accommodate the result. Also, maximum array and vector lengths are implementation dependent. Interfacing with the operating system is a bit murky, and implementations surely differ in handling of errors there.