You're right, at first glance a wiki seems to serve pretty much the same purpose as the website, and in fact they've both got a lot of the same content in them so why bother?. I've built a new wiki at every job I've had for the last.. 15 years or so? and whilst the website is a great way of storing and sharing bits of information and code snippets I found that I wasn't publishing articles that I had because I'd not gotten around to finding an image to go with it or I'd a chunk of code and hadn't written an article to explain it. It's exactly that barrier to 'full documentation' that wikis overcome, they can be excellent collaborative tools when deployed in a team and they can also work as scrappy notebooks if you've got one to yourself, knocking up a structure that makes sense to you and hanging information on it - I needed a wiki for me personally that I could access from anywhere.
There are lots of excellent propositions for wikis online and a lot of them are free as long as you don't want to share your wiki with anyone - that said if you did then there are always ways that could happen. So I looked around and tried a few out, some have excellent real-time document collaboration so that you can see what other people are typing into a document you've got open to edit as they type it! others plugged into software that I'm already using etc.. The problem with all of these however was the price - if I decided later that I wanted to share my wiki with anyone then I'd have to pay around $5 pcm per user (if I paid annually) and they'd have to sign up to whichever service it was that was offering it as well so the market had let me down for what I wanted at a price that I thought was reasonable
Exactly, an afternoon's worth of googling and some research into how to FTP to my site again (should be on here soon) and this is an implementation of TikiWiki, an open-source wiki system that you can install on your web servers, configure and run with! I can mark as many areas as private as I like, create custom user security groups, allow or disallow comments on articles and add as many users as I like all for free! Once I'd installed it and everything I realised that there wasn't any real reason not to have a lot of it accessible to the wide open web and the duplication is just so that I can search one area and have access to everything.
It really goes to show that if you're willing to get your hands a bit dirty with the details and aren't afraid of a bit of research life can be much easier and cheaper!