We have a choice on the menu: deterministic or stochastic modeling of S[t].
In a deterministic model, S[t] is a definite function of the continuous parameter \\(t\\). Once the initial condition is specified, by giving a value for S, then the future values of S[t] are uniquely determined.
This is a "flow." (Semi-flow actually, as S[t] is defined for non-negative t.)