The Sasanian Empire and the Persian Empire are closely related but are not exactly the same. The term ‘Persian Empire’ often refers to various ancient empires that have emerged in the region of Persia (modern-day Iran), with the Achaemenid Empire being one of the most well-known examples.
The Sasanian Empire, on the other hand, was a specific dynasty that ruled from 224 to 651 CE and is considered the last empire before the Islamic conquest. It succeeded the Parthian Empire and is significant for its role in the history of Persia and its conflicts with the Roman Empire. The Sasanians aimed to restore the grandeur of the Achaemenid Empire and often portrayed themselves as its successors.
In summary, while the Sasanian Empire is a part of Persian history and heritage, it is distinct from the earlier Persian empires like the Achaemenid, and thus they are not the same.