They should've taught you at school there were no 'real vikings'. The viking concept is largely a 19th century invention, even if the term viking is derived from the Old Norse víkingr it wasn't popularized until the early 1800s. (e.g. by Geijer's poem Vikingen).

The term víkingr referred to pirates, raiders but in some contexts also to traders (journeys didn't seldom involve both). The vast majority of Scandinavians in the Viking Age were not víkingar in any sense, and those who were didn't necessarily self-identity as it. Boasts about being vikings is something you see in the Icelandic stories written well after the Viking Age, but identifying people as vikings is not that commonly attested during the actual era, in runic inscriptions. The term víkingr was by no means limited to Norsemen anyway; speakers of Old Norse used it for raiders coming from the neighboring Slavic, Baltic and Finnic peoples as well. As I said in another thread there's no reason you couldn't just as well call raiders who were Finns, Karelians, Wends, Kuronians and others 'vikings' too. The Scandinavains were not doing anything qualitatively different from others around the Baltic in that era, although they did venture much farther.

'Vikings' were not the people of Scandinavia. Danes were Danes; Swedes were Swedes, Norwegians were Norwegians. On the contrary the sub-national cultural and political were even deeper; A Jute may be Danish but a Jute foremost. People had different dialects, different religious customs, different laws. Just in Scania alone a half-dozen different burial customs have been documented from the Viking Age.

Denmark did not "rule over the rest of Scandinavia" by any account. Denmark itself was not united under a single king until Gorm the Old and Harald Bluetooth in the middle of the Viking Age, in the mid-10th century. And even that is somewhat exaggerated since peripheral parts like Blekinge and Bornholm were probably not fully under Danish rule until another century after that. There was no centralized government worthy of mentioning until well after the Viking Age.

Scandinavian historians don't generally use the term 'vikings' for Scandinavians of the viking age unless specifically referring to raiders (and not always then either). Adjudicating who the 'true vikings' were would be some pointless pissing contest that's got nothing to do with actual history.

(Recommended reading: Fredrik Svanberg's thesis, Decolonizing the Viking Age)