Your application
This is the donut factory. It exists in complete isolation when it is deployed to the internet.
Your API
This is the road. It opens up a pathway to your app, and allows other software applications to communicate with it automatically.
Widgets, packages & plugins
Different vendors may label these as different things, but they all mean the same. Basically it is a bit of configuration that is done by other software in order to a) connect to your API (security, authorization etc); and b) display information from your application in a nice and useful manner.
It’s worth noting that even though the widgets/packages/plugins are displayed by other software (such as SalesForce), your own developers are often able to build them themselves and upload or install them using special tools provided by the vendor.