Was the Frankkish [sic] Empire and the Carolingian Empire the same?

Your understanding is basically correct, I suppose.

There were two dynasties who ruled the Frankish kingdom,, namely 1) the Merovingians (481?-751) and 2) the Carolingians (751-888/ 987), and Charlemagne belonged to the latter dynasty.

Charlemagne was the first among the Carolingians who was crowned (by the Pope) as an emperor, so, one might assume that there had not been such a 'Frankish Empire' before Charlemagne.

The contemporary usage of the Empire (imperium in Latin) was more difficult to define from our modern point of view, however, since early medieval authors sometimes called the dominion of powerful ruler, not necessarily with the emperor, who ruled diverse groups of people (like the emperor of the Roman Empire) as 'Empire', though even without the emperor.

Some modern European languages like German Reich can also be used to denote both the kingdom and the empire (perhaps my explanation is oversimplified, though), so some translations might be a bit confusing.

Reference:

• Smith, Julia M. G. Europe after Rome: A New Cultural History 500-1000. Oxford: OUP, 2005.