As for their ethnicities: both were Germans (speaking an old German dialect; the term "German"/"deutsch" was developed in the 10th and 11th century). Charlemagne was a Frank, Otto a Saxon. Both were crowned "Frankish kings". When Otto invaded Italy he also took on the same title as Charlemagne "Rex Francorum et Langobadorum". In Otto's time the Frankish kingdom was seen as split but not necessarily as two separate entities. Even Henry II spoke of unifying the Frankish kingdom.

Now the Holy Roman Empire was a totally different concept. It was thought that the Roman Empire of antiquity never really fell apart. It just shifted from the Romans to the Greeks and then to the Franks/Germans. There was a biblical prophecy in Daniel 2 which states that there were to come 4 empires until the end of the world basically. The Roman one was seen as the last and (since it was around when Jesus lived) the only legitimate (=Christian) empire.

So medieval scholars believed that the Roman empire couldn't have fallen since the earth was still around. In that sense Otto held the same office as Charlemagne who held the same office as Constantine or Augustus.

Furthermore, it's a completely modern viewpoint that Charlemagne was anything different than the later Holy Roman (German) Emperors. In medieval and Early modern times people in Germany didn't see it that way. Charlemagne was of course seen as one of their kings/emperors. You can even see it in the numbering of kings: Charlemagne is counted as Charles I, Charles VII of House Wittelsbach would be the last of that name. Otto III found and opened Charlemagne's grave, Frederick Barbarossa canonized him thus making his own emperorship more "holy". (He even introduced the "Holy" in the Empire's title).

I would say Charlemagne was by all means the "first Holy Roman Emperor" but the "Holy Roman Empire" as a realm of its own rights rather then a mere concept was something that developed over a couple of centuries.

In 962 A.D., Otto I was crowned Emperor of the Romans, like Charlemagne before him. What that title essentially claims, is a history going back to the very first Roman Emperor: Augustus, who technically never was crowned emperor.

Now, modern historians tend to recognise that what was going on around 1 A.D. in terms of political structure had very little to do with what was going around 1000 A.D., so they draw lines in the sand to determine key transitional moments, and decide that what's before the line is one kind of empire, and what's after the line is an entirely different kind of thing.

The thing is, there's plenty of room to disagree on what lines we draw where. A lot of historians draw a line between the Carolingian empire and the Holy Roman Empire, and tend to have the Holy Roman Empire start with Otto I's coronation as emperor in 966. Some people think that this particular line in the sand isn't particularly usefull, and consider it to effectively be the Holy Roman Empire from Charlemagne's coronation. There's some merit to both views, but personally I tend to see relevance in the distinction.