Why were the leaders of the Roman Empire sometimes called Kings instead of Emperors?

These titles (in English) refer to rulers from different periods of time. Rome started being ruled by leaders using the title 'rex' (king), some known only from legend, some list in the mists of time. This title was used until 509 BCE, when Tarquinius Superbus was overthrown, and a Republic set up. In this period, control of various facets of society were distributed among a number of people, with various titles, and no one person considered to be at the top.

https://en.wikipedia.org/wiki/King_of_Rome

Then in 27 BCE Octavian once again became a single supreme ruler, and adopted the title of Caesar Augustus.

The term emperor is a modern convention, and did not exist as such during the Empire. When a given Roman is described as becoming emperor in English, it generally reflects his accession as augustus, and later as basileus. Another title used was imperator, originally a military honorific, and caesar, originally a cognomen. Early emperors also used the title princeps ("first one") alongside other Republican titles, notably consul and pontifex maximus.

https://en.wikipedia.org/wiki/Roman_emperor