An HTTP server will always be required to fulfill requests from browsers or other clients that make use of communication by HTTP protocol.
One such server is Apache, which is one of the components of XAMPP. As far as I know, in certain types of hosting plans the provider cited uses Apache and in others Microsoft IIS. They may use other things in certain situations.
XAMPP is usually used only during the site development process.
Certainly they have not installed XAMPP. This is a collection of software that facilitates laypeople to use more easily. They may even have the same components installed there, but otherwise. There are professionals who know how to install and operate everything in a personalized way and do not need anything so ready.
Remember that XAMPP is just one of those Bundles of software for web development and can use other components.
It is possible for the application itself to function as an HTTP server, but it is not usually the case for most of them and especially you will not do this in these shared hosts. This is something much more advanced and you need to have control over the "hosting" environment, plus much knowledge of what you are doing.
If you have other specific questions, open other questions.
Xampp is not an http server, xampp is a package of programs that combines apache, mysql, php and perl. Yes online servers use apache or ngnix or lighttpd. A server looks like a normal computer, however the infra is different, the operating system is aimed at servers and often it is virtualized (Shared or vps) and use apache (or ngnix or lighttpd). If it is a Java application it can use Tomcat or jboss (it has been some time not using), usually these servers are "like-Unix", there are also windows servers that use IIS generally.
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