The 0844 Wizard App requires you to have both credit in the App and available minutes/credit on your mobile phone package.
It works like this:
You dial an 0844 number. The app will tell you what it would normally cost you (an average across all major networks), It will also tell you what it will cost you in Wizard credit .
You then decide you're happy to make the call.
The 0844 Wizard dials and connects to a local rate number (01,02 or 03*) which in turn (the magic part) connects you to the 0844 number you want.
The cost of the local rate connection is taken from your network minutes (the call your phone appears to make.) The call charge for calling the 0844 number (The Wizardry bit) comes out of your Wizard Account.