Do the papers go through the same process when submitted through open access This question is in reference to my question here How to know which journal is open access?

I came to know from my previous question that there are journals which are hybrid journals i.e. they support open access  and at the same time they have issues which dont charge fees from the author.

Now the question is what is the difference in publication process of the two ways in the same journal?

Suppose that I submit a paper in the journal "Discrete Maths" which supports both ways.
So what will be the process of my paper getting accepted/rejected go through when I submit through open access and when I dont submit through open access?

Does the paper go through the same process if I pay the fee or it goes through a different process?

And if it goes through the same tedious process why should the authors pay a large sum of money for it?

I am completely new in this field.So any help will be beneficial.
Open access fee payment is after the paper is accepted. This is to prevent conflict of interest. It means peer review is conducted without knowing whether the paper is open access, and it means the editorial board / publisher is under no extra incentive to accept the paper because of the article processing charge.

In other words, if you submit your paper to Discrete Maths, you should make it all the way to the decision stage (i.e. an accept/reject decision) before you are asked whether you want to make your paper open access. If you say yes, then the production process changes - for example the publisher will use a different imprint on the first page that says you continue to hold the copyright. But that happens after the decision stage. Before it, everything remains the same.

As for why pay a large sum of money for open access: open access is not meant as a shortcut to skip peer review, it's meant as a way to make your paper publicly visible for free. If you publish something in a subscription journal, only those who subscribe to the journal can read it. If you publish something open access, anyone can read it. The core "idea" behind open access is that scientific research should be free to help progress humanity's knowledge as a whole. You can read more about it on the Wikipedia page.