php-saml is a toolkit for making your application a service provider (i.e. able to accept Responses/Assertions from IdPs) so that users can single sign-on to your application.

SimpleSAMLphp is a framework/application for creating your own SAMl IdP (i.e. able to send Responses/Assertions to service providers) so that your users (e.g. in an enterprise) can login once and then single sign-on to the rest of your applications.