We can write the formulation for the buttlerfly function applied in FFT as
\begin{align*}y_0 &= x_0 + x_1,\\ y_1 &= x_0 - x_1. \end{align*}
As seen here.
For FFT (Fast Fourier Transform) we have that $x_0$ and $x_1$ are complex numbers, then the addition and subtraction operations are complex operations.
We can use the same formulation in NTT (Number Theoretic Transform), just replacing the complex operations by modular operations.
How to do the same conversion for radix-4 and radix-8, from FFT butterfly to NTT?
I could derivate the formula for radix-4 NTT following this.
In radix-4, each butterfly's element is given by
$$Y_{p,q} = \sum_{l=0}^3\left[W_N^{l\cdot q}X\left(l,q\right)\right]W_4^{l\cdot p}.$$
This way, let $P$ be the prime that generates the finite field used by NTT and $W_4$ and $WInv_4$ respectively it's twiddle factors for forward and inverse NTT. This way, the formulation of a radix-4 butterfly on forward NTT is
\begin{align*} y_0 & = x_0 + x_1 + x_2 + x_3,\\ y_1 & = x_0 + W_4\cdot x_1 - x_2 - W_4\cdot x_3, \\ y_2 & = x_0 - x_1 + x_2 - x3,\\ y_3 & = x_0 - W_4\cdot x_1 - x_2 + W_4\cdot x_3. \end{align*}
For inverse NTT we just replace $W_4$ by $WInv_4$.