Yes, the Worlds you can choose to play on are the same in both the free trial and the full versions of FINAL FANTASY XIV Online.

Certain Worlds may have character creation restrictions depending on the current population. Please visit the following page for current character creation restrictions:

https://na.finalfantasyxiv.com/lodestone/worldstatus/

For other free trial-related questions and concerns, check our Free Trial FAQ at http://support.na.square-enix.com/faqarticle.php?id=5382&la=1&kid=70929&ret=main