Ejectment actions are brought when a tenant, or other person staying in the rental property, refuses to vacate and claims to have an ownership interest or other types of equitable in the rental property and meet other criteria. A typical situation is when a Lease includes an Option to Purchase clause, and the tenant claims to have exercised this Option and paid some of the money toward the purchase price or at least resided at the property for a significant period of time paying rent. 
There are other scenarios that would require an Ejectment Lawsuit and not an Eviction. Like eviction cases, at the conclusion of the Ejectment Lawsuit, a Writ of Possession is issued by the Clerk of Court that requires the Sheriff to remove the Defendants/Tenants.
Ejectment disputes are set forth in Florida Statutes Chapter 66.011 to 66.101. The most important issue to be proven in an ejectment action is the right to title to the property. That means the plaintiff bringing an ejectment action has to show they are the proper record title holder of the real estate. Proving the chain of title in the plaintiff can be complicated where the property has not been transferred for many years or easement issues or property boundaries controversies have arisen.