That pretty much sums it up. but in laymans terms...
HTML is Clientside - the code is sent to the browser of a viewer and is decoded by the browser of choice. This is why different browsers display websites differently.
PHP is Serverside - its code is never sent to the browser of a website viewer. The server's software runs the code and everything happens without the viewer seeing it.
and...
HTML is incharge of Design/Layout of a website
PHP is incharge of data management
Other Clientside coding includes CSS, DHTML, and Javascript
Other Serverside coding includes Perl, ASP, and... umm... yes... =