Reflection Coefficient with Electric Field and Voltage
A couple weeks ago, I answered one of your earlier questions like this:

Remember that when we defined the electrostatic potential difference (aka &quot;voltage&quot;),
$$V=-\int \vec{E}\cdot d\vec\ell,$$
we called it the electrostatic potential difference because it is only strictly valid in electrostatics. When we use this concept in AC circuits, we're using it as an approximation only (usually described as the lumped circuit approximation). In particular, in the presence of time-varying magnetic fields, we can't count on this \$V\$ to be independent of the path over which we take the integral.
In transmission lines, we are definitely dealing with time-varying magnetic fields, so we can't expect the electrostatic potential difference to be well defined.
We define an approximate potential at a point along the transmission line as the negative integral of the electric field from one conductor to the other at that point.

[emphasis added]
The voltage at a point on a transmission line is defined by an integral of the electric field between the conductors at that point. So if you double the electric field, you double the voltage, or if you halve the electric field you halve the voltage.
So your two definitions of the reflection coefficient are equivalent, provided the transmission line is well-behaved enough to let you actually define a voltage on it.