There are park-to-park buses.
For the MK, those buses are located at the TTC. This means that you will need to take the Monorail to the TTC to catch a Studios or DAK bus, or the Epcot monorail. And likewise, you'll need to catch a TTC bus from DAK/Studios to get to MK.
Between Studios and Epcot there is a bus and a boat. The boat will service the World Showcase of Epcot, and the bus services Future World (front of park).
There is *NO* park transportation to or from Downtown Disney.