Use CTRL+S to save your project.
You can also use the Save Button in the top settings bar :
A saved project can be reloaded on your computer and will load the tools in your own database and the CADs at their path in your computer.
You can also Export your project. An exported project is shipped with its CADs and the tools that it is using and it is then possible to send them to another user of Fuzzy Studio. Otherwise when you are only saving the project, the tools and the CADs used in the project are only present on your computer, thus when you open the project on another computer those elements would be missing.