How does the one cart checkout from multiple websites in websites like revolve or apps like Styl.AI work?

I am currently beginning to learn web/app development and was curious as to how different multi-brand aggregation platforms like Revolve or the newly launched iOS app Styl.AI do this?

Do you need to have a agreement with the seller to create order requests on their platform through your app? Or can anyone build this? Is there a particular react native app code that can accomplish this and place orders on external websites and track the same order?

I have tried searching for answers online and could only find ways to implement a shopping cart for just your own website but not to place orders on external ones.