Two functions which are identical always return the same result for the same input. That's the definition of a function. Consider that the state of the computer is also an input to the function: if the random seed is the same for both functions, they do return the same results.

If two functions have the same input (including the exact same environmental states) but do not return the same results (also consider changes to the environment to be "outputs") then they are not the same functions.