The first triplet stores the snapshot of interpreter state in an opaque token returned by Tcl_SaveInterpState. That token value may then be passed back to one of Tcl_RestoreInterpState or Tcl_DiscardInterpState, depending on whether the interp state is to be restored. So long as one of the latter two routines is called, Tcl will take care of memory management.
The second triplet stores the snapshot of only the interpreter result (not its complete state) in memory allocated by the caller. These routines are passed a pointer to a Tcl_SavedResult structure that is used to store enough information to restore the interpreter result. This structure can be allocated on the stack of the calling procedure. These routines do not save the state of any error information in the interpreter (e.g. the -errorcode or -errorinfo return options, when an error is in progress).
Because the routines Tcl_SaveInterpState, Tcl_RestoreInterpState, and Tcl_DiscardInterpState perform a superset of the functions provided by the other routines, any new code should only make use of the more powerful routines. The older, weaker routines Tcl_SaveResult, Tcl_RestoreResult, and Tcl_DiscardResult continue to exist only for the sake of existing programs that may already be using them.
Tcl_SaveInterpState takes a snapshot of those portions of interpreter state that make up the full result of script evaluation. This include the interpreter result, the return code (passed in as the status argument, and any return options, including -errorinfo and -errorcode when an error is in progress. This snapshot is returned as an opaque token of type Tcl_InterpState. The call to Tcl_SaveInterpState does not itself change the state of the interpreter. Unlike Tcl_SaveResult, it does not reset the interpreter.
Tcl_RestoreInterpState accepts a Tcl_InterpState token previously returned by Tcl_SaveInterpState and restores the state of the interp to the state held in that snapshot. The return value of Tcl_RestoreInterpState is the status value originally passed to Tcl_SaveInterpState when the snapshot token was created.
Tcl_DiscardInterpState is called to release a Tcl_InterpState token previously returned by Tcl_SaveInterpState when that snapshot is not to be restored to an interp.
The Tcl_InterpState token returned by Tcl_SaveInterpState must eventually be passed to either Tcl_RestoreInterpState or Tcl_DiscardInterpState to avoid a memory leak. Once the Tcl_InterpState token is passed to one of them, the token is no longer valid and should not be used anymore.
Tcl_SaveResult moves the string and object results of interp into the location specified by statePtr. Tcl_SaveResult clears the result for interp and leaves the result in its normal empty initialized state.
Tcl_RestoreResult moves the string and object results from statePtr back into interp. Any result or error that was already in the interpreter will be cleared. The statePtr is left in an uninitialized state and cannot be used until another call to Tcl_SaveResult.
Tcl_DiscardResult releases the saved interpreter state stored at statePtr. The state structure is left in an uninitialized state and cannot be used until another call to Tcl_SaveResult.
Once Tcl_SaveResult is called to save the interpreter result, either Tcl_RestoreResult or Tcl_DiscardResult must be called to properly clean up the memory associated with the saved state.