yes - you have two options there. You can build separate sites with new layouts etc, or you can have all the sites run from the same code base, where the content is substituted dynamically. There are many ways to do that, but I'd recommend a data-driven solution with in-memory caching of all the content for maximum speed & flexibility.
For the storage of the "translated" phrases, use SQLite or Redis.
"Internationalization" is a well-covered topic in webmastery; it's often shortened to "i18n" so when you're searching for solutions, try searching for that too.
Once your i18n solution is established, you'll have the infrastrcture to to translate your content into other languages too.