That Transportation Wizard is a bit dated, and from what I've seen of it... not that accurate.
Disney Transportation is fairly easy once you understand how it works.
There will be direct transportation from ALL Disney Resorts to All four theme parks, plus Downtown Disney, Typhoon Lagoon, and Blizzard Beach. No transfers. Busses start running at 7am for Character Breakfasts, and for the parks, 1 hour prior to the parks opening. Monorails start at 7am for Breakfast, 7:30 for MK, and 8:00 for Epcot. Boats typically start at 8:30.
In addition, there will be return transportation from all four theme parks, Downtown Disney, and both water parks going back to your Disney resort. Once again, no transfers. Busses and monorails will run back to the resort until that particular park is clear of all guests. (Note that boats stop service 1hr after the park closes.)
Each theme park also has "Park Hopper" transportation. These busses provide transportation to and from Epcot, Studios, Animal Kingdom, and TTC (MK).
The only park that has transportation to Downtown Disney is the Studios. (Epcot was discontinued due to lack of ridership, and TTC was discontinued because it was being abused by Hotel Plaza guests avoiding thier own busses.) Note that the Studios bus is only a "Test" bus... and provides ONE WAY service to Pleasure Island. There is NO return bus.
Alternativly, the only way to get to Downtown Disney from a Theme Park is to go to a Disney Resort, and transfer there.
For Resort to Resort... Each theme park acts like a "Hub"... To go from one resort to another, you will transfer at a hub.
(All of this information is of course subject to change at any moment, as Disney is always trying to improve service.)