Hi,
If you want to request a page with AJAX, you can use the ajax functions of javascript:
www.sitepoint.com/guide-vanilla-ajax-without-jquery/
On Joomla, if you want to call a page without the modules and template around the main area, you can add the parameter &tmpl=component
For example:
demo.hikashop.com/index.php/en/hikashop/...sting/display-in-div
demo.hikashop.com/index.php/en/hikashop/...n-div?tmpl=component
So you can edit the HikaShop views as explained in the link Jerome gave you, and add there your button to switch the interface, along with the javascript it would trigger when the user click on the button to call the same page URL with the tmpl parameter and replace the main area content with what is sent back by the AJAX.
Then, in the view file, you can add custom PHP to display the listing differently based on that tmpl parameter value.
I hope it's clear. As Jerome explained, we can't provide a ready made solution as this requires proper development and is outside of the scope of this user forum.