The main difference is in functionality, although HTML5 is a major advance in functionality.
PHP uses server-side scripting that most web hosts provide as standard. PHP scripting uses HTML for appearance, but allows easy access to all kinds of extra functions and data handling. PHP also allows you to easily compile pages from a set of elements which can be quickly and easily altered in order to change them on ALL pages of a site.
For example, if you have a header, main menu and footer (all separate pages) you can create your regular pages by using PHP to import those elements into a template that might appear like this:
(from the header master page)
(from the main menu master page)
(from the footer master page).
If you need to change your header, menu or footer on all pages of your site, you can simply make those changes on the master pages and every page will reflect those changes.
Many content management systems (CMSs) use PHP, including WordPress.
Hope this helps. (I've kept it really basic.)