How do I know if I am using Creo Illustrate, Or Creo Illustrate Essentials?

It says in the title bar of the application, it will either say:

Illustration name.c3di - PTC Creo Illustrate

or

illustration name.c3di - PTC Creo Illustrate Essentials

It will also tell you in the 'About PTC Creo Illustrate' dialog which is accessible via File>Help>About PTC Creo Illustrate.

Lastly if you are running essentials you won't have the 'Advanced' button in the animation ribbon.