This is referring to ancient times. I may be completely wrong but I always thought that the Iberian peninsula was modern day Spain. But then I saw on a map recently that Iberia is actually to the easy of Greece. Could anyone clear up my confusion on the difference? Are they related?
There are in fact two Iberias, one the peninsula in the southwest corner of Europe, the other in modern-day Georgia (another name that's sometimes confusing). Their commonality is entirely coincidental--the eastern Iberia's etymology is uncertain, but their being related is unlikely.
As for Iberia vs. Hispania, the former is just the Greek name for the peninsula, and Hispania is the Roman name for the peninsula, likely derived from a term used by their Carthaginian or Iberian predecessors.
Also, for trivia's sake, there's also two Galicias--one in northwestern Spain, the other in eastern Europe. It's possible those names are related, by way of "Celt" which is similarly the origin of the names of places like Gaul and Wales.