How does it work and how is a payment system added to the site?

Question

I never understood how on these sites (e-commerce) purchases are made between the user and the payment system and many of them the payment systems differentiate what gives to imply that there are various types of payment systems in the market.

I own an online site and want to start selling some projects but don’t know where to start and worse than I don’t know how it works or how to add a payment system on my site.

I have other related doubts:

It is some kind of API of a bank or a company that is added on the site?

Or to be more precise I could create a payment system on my site from scratch?

These types of payment systems use server-side languages such as PHP?

Answer 1

"It is some kind of API of a bank or a company that is added on the site?"
Yes is what is usually done, some examples are "Pagseguro", "Mercadopago" and "Paypal".

Or to be more precise I could create a payment system on my site from scratch?
It is not recommended because it has to implement many things of security in dealing with sensitive data such as bank and credit card data. It is better to rely on services that already provide several options of payment ready, as boleto, TED/PIX, debit account or credit card, and even if you wanted to make your own system, will have to implement each of them individually.

These types of payment systems use server-side languages such as PHP?
Yes it has to be on the server side, but if you are going to use a service that already exists, the language does not matter, because if it is an API, the important thing is to be able to make calls HTTP/HTTPS to this API, which can be implemented in any language that supports the protocol HTTP and other requirements, such as REST.

Here on the site has good questions to help you about:

Paying
Mercadopago
Paypal
Payment gateway
What is REST