The difference between the global and local costmap is that the global planner uses the global costmap to generate a long-term plan while the local planner uses the local costmap to generate a short-term plan. There are many different ways to configure the two costmaps, but in the tutorials only the global costmap is configured to use a map while the local planner operates in the odometric frame.
Setting the "static_map" parameter to true just means that you'll be taking an outside map source for navigation. That map could come from SLAM or it could come from a source like the map_server. You shouldn't have to change the way you've configured the navigation stack to run SLAM, you'll just replace the map_server with your SLAM algorithm of choice.
To see an example of the navigation stack running with SLAM, you might want to check out the navigation_stage package. Specifically, you'll be interested in the move_base_gmapping_5cm.launch file.
The "static_map" parameter is, admittedly, a bit poorly named. It should probably be something like "external_map" instead, but there are legacy reasons for why it has its current name. There was a time where the navigation stack couldn't support dynamically changing maps, but now it handles them just fine.
