The caption of a picture here says that "The session of the Grand Council of 9 May 1936, where the Empire was proclaimed". What did it mean in practice that Italy was proclaimed an "Empire"?
According to that obscure source, Wikipedia, on 9 May 1936 King Victor Emmanuel III of Italy was proclaimed Emperor of Ethiopia. https://en.wikipedia.org/wiki/Victor_Emmanuel_III_of_Italy1
Thus I guess that the only empire proclaimed by the Fascist government of Italy on 9 May 1936 was the Italian Empire of Ethiopia. It is unlikely that the Fascists would proclaim 2 empires on the same day. And I have never read of any formal empire of Italy instead of mere informal descriptions of Italian colonial possessions as an empire.
Here is the title of Victor Emmanuel III from 1936 to 1939:
King of Italy;
Emperor of Ethiopia;
-  Ethiopia
The Italians conquered the Empire of Ethiopia (1936).
(June 1936) [4: n° 146; 25 giugno 1936; Doc.# 1143]
< Victor-Emmanuel III (+1947), King of Italy [1900-1946], of Albania [1939-1943]; Emperor of Ethiopia [1936-1943] >
Vittorio Emanuele III per grazia di Dio e per volontà della Nazione Re d’Italia
And here is his title from 1939 to 1943:
King of Italy, Albania;
Emperor of Ethiopia;
-  Albania
The Italians conquered the Kingdom of Albania (1939).
(June 1939) [4: n° 203; 31 agosto 1939; Doc.# 1229]
< Victor-Emmanuel III (+1947), King of Italy [1900-1946], of Albania [1939-
1943]; Emperor of Ethiopia [1936-1943] >
Vittorio Emanuele III per grazia di Dio e per volontà della nazione Re d'Italia
e di Albania
Thus we see that in 1936 King Victor Emmanuel III took the title of Emperor of Ethiopia and used it until 1943, and that he did not take a title of Emperor of Italy in 1936.
What does it mean, in practice, that North Korea calls itself the "Democratic People's Republic of Korea"?
It's a title, a meaningless proclamation, but little else. Of course, the fascist governments of that era understood that inspirational dreams of reclaiming past glory do matter to a country's citizens, and that proclamation was part of the Mussolini government's pitch about reclaiming Italy's glory days of the Roman Empire, but that was really the extent of it. It was nothing more than public relations or propaganda, or whatever you wish to call it.