Two Minimax AIs playing against each other

Question

I am trying to have my Minimax AI chess players play against each other.

I was a bit confused about an implementation detail.

Let's call black my first minimax AI chess player that plays first.

white is the other minimax AI that goes second.

My question s about the turn. Should black maximize and white minimize OR should they just try to maximize when at their respective turns, with the evaluation function flipped?

I have thought up of two ways to go about this. I have a feeling that they are doing the same thing, but just wasn't sure whether I am right or the two solutions are in fact doing something different.

First solution:

Instantiate a MinimaxAI object for black and white separately. Make sure that black's evaluation function is the opposite of white. For a simple example, the object black's evaluation function is
number of black pieces on board - number of whites on board.

The white object will have an opposite evaluation function number of white pieces on board - number of blacks on board.

Now, when each object takes turns to call the same get_next_move method, they will both be the maximizing player of the minimax algorithm.

Second solution:

Instantiate one Minimax AI object ai to be used by both the black and the white as they alternate turns. black and white will have the same evaluation function
number of white pieces on board - number of blacks on board

Assuming white always goes first in chess, when white calls ai.get_next_move with an even turn number, it will be given the maximizing player role. On the other hand, when black calls ai.get_next_move with an odd turn number, it will be given the minimizing player role.

(this is what I have so far)

I think both should result in the same behavior, but it is more of a feeling than an educated opinion. Please let me know if my feeling is actually correct or not. A semi-formal reasoning process will be welcome!