Like Joomla, WordPress is another Content Management Driven web site designer.
Although it operates in much the same way, ie. database driven content served up as web pages, their design philosophy is different.
Arguably, any Joomla site can be made to look like a WordPress site and visaversa, but depending on what you want will decide which CMS to use.
So when we are discussing your business and target markets, we will also be thinking about HOW your information will go to the WWW.