I can do it using AJAX. But I can also do it using a REST call.
Um, no. Those two are completely orthogonal. If you want to update your page with data you have to get from a server, you will do it using AJAX. There is no other way. And that AJAX call can use REST, or something else.
My problem is i really dont get the difference between REST and an HTTP browser request.(a.k.a a form submit). I have looked at formal definitions of REST and it seems like a HTTP request.
A REST call is an HTTP request, always. Though it can be used to handle regular browser calls (like form submits) and return full HTML pages, it's usually used to handle API calls that return only data (usually in JSON format).
So why it has a separate name?
Because REST is a specific style of using HTTP, arguably using it as it was originally meant to be used, but which most people didn't "get" and was thus rarely used for almost 2 decades.
Specifically, REST means encoding which entity you want to retrieve or manipulate in the URL itself (usually via an ID) and encoding what action you want to perform on it in the HTTP method used (GET for retrieving, POST for changing, PUT for creating, DELETE for deleting).