A gadget refers to a small mechanical device or tool, especially an ingenious or novel one.
A widget carries the same thought, but adds that the name of the device or tool is generally unknown or unspecified.
Another definition of widget is added in relationship to an application that enables the user to perform a function or access a service.
Here is where we find an interesting twist in leadership.
Figuratively speaking, leaders serve as widgets. They carry the responsibility of enabling others to do the work or access the tools needed to fulfill the task.
The idea introduces a level of empowerment that helps others reach their greatest potential.