Hi @Akanrat,
If the user is authenticated then yes it will be the same. Because for authenticated user cart is fetched from the database.
I think you are getting confused, I am just sharing a thread that will help you,
Actually, this is a cross-domain, you need to send the cookies so that session can be tracked. I am sharing with you a thread that can help you just try to send cookies in ajax request and it will work.
https://stackoverflow.com/questions/29417518/how-can-set-cookie-with-ajax-jquery/29417575#29417575
https://symfonycasts.com/screencast/reactjs/api-authentication