If served an eviction notice in the state of Florida, do you have to move or if you pay the rent after eviction notice is served do you stillhave to move out of the aprtment. I told the landlord that I can't pay my rent until Thursday but she told me the home office said if I didn't pay the rent by Monday eviction notice will be served

Depends are you on a lease, if so what does the lease say, if on month to month rental, they can evict for any or no reason in most places with just a 30 day notice.

Most eviction notice are a pay or quit, which means if you pay the rent plus all of the late charges and penalties you don't have to leave.
So it will depend on the notice given