What is the relationship that connects potential difference between two points and the strength of the electric field between those two points?
To pick up on @mike stone, in general there is none.
For instance, in a region where the electric field is constant in magnitude and direction, the potential difference between two points is $V(\vec r_1)-V(r_2)=-\vec E\cdot (\vec r_1-\vec r_2)$. This can be $0$ if $\vec E$ is perpendicular to $\vec r_1-\vec r_2$.
More generally there is a range of possible values depending on the angle between $\vec E$ and the difference $\vec r_1- \vec r_2$. Note here that I have assumed above $\vec E$ is constant, meaning no difference in $\vec E$ between $\vec r_1$ and $\vec r_2$. This is enough to show there is no connection between potential difference and field difference in this special case.
This holds even more strongly when the field varies with position; the key observation is that the scalar product $\vec E\cdot d\vec \ell$ produces a geometrical factor that makes it impossible to link potential and fields differences in general.