CMS (content management system) is an application and unlike a framework it provides you higher level developed architecture for working with content - publishing, editing, organizing and deleting. Simple difference between framework and CMS is that CMS is built with framework.
There are many open source CMSes built with PHP, that might be worth picking for your project since they speed up the project delivery and they have large communities behind them which can help you a lot.
Which CMS is right for your project, is quite honestly impossible to answer in general. You must know the benefits and limitations of them before creating a project.
Some of the recommended open source CMSes built with PHP:
CMS is usually a complete out of the box solution. Content management framework (CMF) on the other hand is a system, which uses reusable components and is a level between a framework and a CMS. It enables you to make your CMS more customized. Many CMSes listed above have characteristics of CMF as well however the following examples are some more notable content management frameworks by the definition: