I understand the difference, when expressed, has to do with the peoples a government seeks to exert domination over, its citizens (authoritarianism) or the outside world (totalitarianism.)
Rather than comparing theoretical definitions, let's look for the rare cases where recognizable experts distinguish between the two with factual regimes.
Wikipedia calls Franz Borkenau one of the pioneers in totalitarianism theory. In the 1950's he wrote a report for the U.S. State Department. The report began:
In the view of this writer a profound conflict between the Communist regimes of Russia and of China is in the long run as certain as anything
predictable in politics. Its necessity can be demonstrated by a very simple formula. Totalitarian regimes live by an inherent urge to establish their absolute, “totalitarian” control as far as they can. A totalitarian regime, and more especially the Russian regime, is striving for absolute world domination. It therefore cannot have genuine allies, but must try to subjugate everything within its reach. This is
incompatible with the obvious Chinese quest for national independence.
[Published in J. Tashjean, “The Sino-Soviet Split: Borkenau’s Predictive Analysis of 1952.” China Quarterly, No. 94 (1983)]
Six decades later, Joseph Sassoon, in Saddam Hussein’s Ba‘th Party: Inside an Authoritarian Regime (New York: Cambridge University Press, 2012), compares Hussein with Stalin, concluding that while many similarities exist, Saddam’s government was authoritarian, not totalitarian, since Stalin’s control over the military won wars, and Saddam’s did not. Sassoon's book has received unofficial recognition within the US intelligence community.
Based on these usages, it might be reasonable to associate totalitarianism with empire building, and assert the Roman Empire exhibited totalitarianism but less authoritarianism, because Roman citizens were (generally) treated with substantial deference both by their own government, and in any country in their realm of influence.