Numerical Analysis - natural cubic spline and clamped cubin spline

Question

a question from first exam period (A).
True or false ( it is false, but I want to understand ).
Given the following intersection points $x_0, x_1,...,x_n$ (interpolation nodes ) and the values of those points $y_0, y_1, ..., y_n)$ and you calculate the spline polynomial cubic appropriate.
claim: natural cubic spline and clampled cubin spline give the same approximate value at the open region $x\in (x_0, x_n)$.
The answer is False, but my question is something different. if $x\in [x_0, x_n]$, what would the answer be, and why?
About $x\in (x_0, x_n)$ I thought it is false ( and was right ) because the boundary value problem at each spline is different at second derivative ( $s''(x)=0$ at first and last index of natural and at clamped it is not ).
But if the range moves to including $x_0$ and $x_n$, how does it differ? will the question, still remain False or be True?