So far, I could not find an exact answer, many of the well-known empires were actually ruled by a king/queen instead of emperor/empress (British/Spanish empires). So what is the line that separates between those two?
Additional question: some Lithuanian historians claim the Grand Duchy of Lithuania was actually an empire at its peak. While it never had that title (kingdom title was also held only for a brief period of time) they claim that Lithuania actually fit the description namely:
It was a sovereign state
It was much larger than any other country in the region
Carries out large-scale territorial expansion
It was a hegemonic state
It was heterogenous in ethnic and cultural terms and had politically dominating ethnocultural minority
At some point its area reached so called "necessary" 1 million square kilometers
Do these claims have any basis or are there any better aspects that define an empire? Thank you and sorry for poor formatting
An Empire does not require the explicit title of "Emperor" to meet the definition. An Empire is any kingdom (or sometimes in the modern definition, it can not even be a monarchy) that rules over other ethnicities spanning a wide geographic area. Empires are always formed through expansionism. It is a political concept and designed to elevate the status of an exceptionally large, diverse and powerful prestigious kingdom.
So for example Lithuania at its peak controlled all of modern-day Belarus, Ukraine, Western Russia, inhabited by the Slavic-Ruthenians and parts of Poland etc. places where ethnic Lithuanians did not live or form any meaningful number. As you wrote Lithuanians became the dominant ethnocultural minority, and their culture influenced all these people, and just look at the modern Belarusians and their adoption of the Pahonia coat of arms (Vytis symbol in Lithuanian). So this territory was taken through conquest and driven by an expansionist zeal. Moreover this territory was very diverse in language and religion. This meets the definition of an "Empire" even though the Lithuanian monarchs styled themselves as Grand-Duke.
Returning to your first few sentences, the title of the sovereign did not necessarily matter. In the case of the British Empire, besides the title King of England and Scotland etc. there was the title Emperor of India used by the British monarchs. It was the imperial colonies which gave Britain its status as an Empire. Compare this to France, and France had natural growth in Europe through conquest and expansion and this gave it an Empire status under Napoleon.
Furthermore there were kingdoms which had the title Emperor, as was the case with the Bulgarian monarchs in the Kingdom of Bulgaria who had the title of Tsar (Slavic for Emperor) instead of Kral. There was a medieval Bulgarian Empire that wasnt that much larger but relative for the time and place, and its strength and relevancy etc., it constituted an Empire in the eyes of its neighbors such as the Byzantines.
In modern times, Empire has come to mean an imperialist entity which is why the term "American Empire" is often thrown around because of the military strength of the US, its diplomatic influence, and its presence throughout the world.