Do both $.ajax and $http use XML HttpRequest internally?

Hey first you need to understand that AJAX and REST are not really to alternatives for your use case. AJAX stands for asynchronous javascript and XML so if you are using javascript to load data after the browser request has finished you are doing AJAX.

REST on the other hand stands for Representational State Transfer call is an HTTP request. 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).

Which one is good?
In this case you have to think about the amount of data used in your request. If you have only few elements you could have them all in your page and just use javascript to show the appropiate ones. A second option could be using a REST call with JSON as respresentation because it's easy to use with javascript and very lightweight which of course would also mean doing AJAX.