Saving a simulation stores all the necessary data to run the simulation on the original computer where it was created. Exporting a simulation, on the other hand, lets you transfer the completed simulation to another computer with Fire Studio installed, while still allowing future edits. Publishing (FS7 Only) a simulation enables you to move it to another computer but restricts any further modifications.
The Save, Export, and Publish buttons can be found on the Slide Panel under the Simulation Display screen, which appears when Fire Studio launches.