Minor question about your formula for Taylor's formula

[iampi31415]

Hey great blogpost here https://adamdjellouli.com/articles/numerical_methods/3_differentiation/central_difference

I do not quite get why you use $\xi$ here and in the other case?

$$f(x+h) = f(x) + hf'(x) + \frac{h^2}{2}f''(x) + \frac{h^3}{6}f^{(3)}(\xi_1)$$

I think in both one should simply put $x$?

That is how Wikipedia show the Taylor Series / Expansion of $f$ at least?

I read a bit and I am aware there is one form of the expansion that uses a Lagrange term I think, and is supposed to be so that one does not write the rest of the sum (a catch all the rest term that given a suitable $\xi$ will make the equality hold).

Well, I hope if the case is the latter a small note could be added? I was just reading out of curiosity though. Thanks!