The Carolingian Empire and the Holy Roman Empire are directly related.

The Carolingian Empire was started by Charlemagne, who descendants then split his territories into several smaller kingdoms but predominantly West and East Francia. West Francia is the forerunner of what we call France, while East Francia was situated predominantly in what we now call Germany.

Over time, East Francia diverged from its supposed 'Francian' identity and its rulers became known as 'King of the Germans'. King Otto of Germany made an alliance with the Pope against King Berengar of Italy, who was hostile to Otto and the Papal States. In return for Otto's support, the Pope agreed to crown Otto as Emperor of the Romans to emphasize Otto's position as defender of Christendom and legitimize his desire to absorb Berengar's domains. This also drew a line to Charlemagne, who himself was crowned 'Emperor of the Romans', as a way of showing Papal support to Charlemagne while renouncing Byzantine influence in the region.

I believe Otto is generally considered to be the founder of the Holy Roman Empire, in terms of establishing the actual state (as much as you could call it a single state) and how it functioned. But as Otto was a successor to Charlemagne you could consider Charlemagne the 'spiritual' founder of the Holy Roman Empire.

So even though there is a distinction between the Carolingian and Holy Roman Empires, the latter is a direct evolution of (the Eastern part) of the former.