Disney Genie is the free service that is offered by default within the My Disney Experience app. It has some basic planning tools that aren't really worthwhile.
Disney Genie+ gives you the opportunity to book slots for the Lightning Lane of various attractions throughout the parks. It is an additional fee per person to use this service. The price history can be found here.
You can also gain access to the Lightning Lane of a few attractions (Avatar Flight of Passage, Cosmic Rewind, TRON, & Rise of the Resistance) without purchasing Genie+ by purchasing an Individual Lightning Lane. This is a separate charge, per person, to skip the line a single time via the Lightning Lane. The price also varies (see the price history here).
In short, either Genie+ or an Individual Lightning Lane get you access to the Lightning Lane.