No Wikipedia is not Wiki. Many people confuse Wikipedia with wiki, but wiki is different from Wikipedia of course both are related to each other in a different way, let me explain this.
Wiki is a web page or web site [group of web pages] where the viewer can edit the contents and save it. Wikipedia is an example , as in Wikipedia you just click edit—> change the contents —> save your changes, as simple as that.Wikipedia is built using a Wiki tool.
So from now on, when you hear someone saying he has a wiki, it means u can change the content in his/her site and save it.