Colonization is a long process- involving the settlement of civilians from the colonial power and the economic exploitation of the 'colonized' area. Colonialism was certainly Mussolini's goal in Ethiopia, he wanted to create an Italian empire to recapture some of the glory lost since the fall of the Roman empire. What he actually accomplished was a bloody and costly military occupation that did little if anything to actually strengthen Italy.

When you hear that Ethiopia was not colonized, it's largely because of the short length of time that Italy occupied Ethiopia, and because the outbreak of WWII quickly overshadowed and ultimately reversed the process of colonization. Although Addis Ababa fell by May 5, 1936, the Italians were challenged by guerrillas frequently over the next several years of occupation. And of course the Ethiopian emperor, Haile Selassie, never formally surrendered and continued to try to convince the League of Nations and later the Allies to free his country. Although the guerrilla conflict had died down by the outbreak of war between Italy and the UK in June of 1940, many Ethiopians proved all too willing to rise up again with the arrival of British forces to the East African theatre. Haile Selassie returned to Addis Ababa five years to the day after having been forced into exile.

Some Italian civilians did move to Ethiopia, and some Ethiopian soldiers did fight (briefly) to defend Italian East Africa from the British (as the Italians, in a classic tactic of colonialism had favored Somali and Muslim minorities over the majority to earn their loyalty). But a five year military occupation is not really what any historian means when they discuss colonialism. No one would call the similarly long occupation of Poland by Nazi Germany colonialism either- even though Hitler invaded in order to have more land for Germans to live on, to exploit local resources, and to spread his ideal vision of society to conquered lands.

This is largely because Italian control was such a short duration, and that the Italians never really exercised anything like a functioning hegemony over Ethiopian society or affairs. It's also that the pre-Italian regime was continuous with the post-WWII regime, which did not happen in any other part of sub-Saharan Africa (leaving aside Sierra Leone and Liberia). Haile Selassie went into exile, but technically his sovereign authority was uninterrupted in the eyes of most other nation-states; he resumed his place at the head of the Ethiopian state after the war until he was deposed in 1975. So in some sense, people might say that Ethiopia was defeated in war, or was invaded, but not colonized, for the same reason that we do not say that France was colonized by Germany in World War II.

Many people play fast and loose with the terms colonialism, colonization and colonized.

In academic discussion it does not merely describe an action where military, political and economic control is established over an area, which is also disconnected from the homeland. That would simply be called a conquest.

It also implies the attempt of integrating the conquered land into an economy serving the "mother state". This can mean creating a base of operations for Trade, or taking new farmland, which was the incentive for colonization before the early modern period. In an economy which could support such a system, simple luxury goods like tobacco and sugar can also warrant establishing colonies.

If a foreign power holds control but does not really do any of that, but rather uses the territory or people in different ways, or simply demands tribute or peace, taxes and obedience, is it really accurate to call it colonization.

As you can imagine, no such process had been completed during the comparatively short time Ethiopia was controlled by the Italian Army, as Grombrindal18 has already pointed out.

African countries that have somewhat changed entirely from these foreign powers are the ones that are usually considered colonised. Look at many of the west and Central African countries, not only do they retain the language of their colonial oppressors but also the currency. The lingua franca of some African countries come from colonialism. In Ethiopia’s case, Italian influence is extremely minuscule as Ethiopia retains most, if not all of its cultural heritage. Amharic is the state language not Italian.

It is also worth noting that for a country to be colonised, it needs to be under full control of the region. Italy really only controlled the capital fully and there was still a lot of guerrilla warfare in Ethiopia against the Italians so arguably the country wasn’t fully taken over nor colonised.