As always in history, answers are the more complicated the simpler a question is. Wikipedia is right with its statement, at least to some extent, on the title 'Cesar' that Augustus is called 'the first Roman Emperor Cesar Augustus' because Octavian/Augustus (63BCE - 14AD) called himself 'Imperator Caesar'). - while my own statement is not wrong either which derives from the imprecision of the English language (other European languages like German are even worth in this respect). We translate lat. 'imperator' as a technical term in the military sense with a commander-in-chief, general, = στρατηγός (cf.: dux, ductor) (Lewis&Short), in the Roman political and cultural sphere with 'a commander, leader, chief, director, ruler, master', and we know it as an epithet of Jupiter (Cic. Verr. 2, 4, 58, § 129: “signum Jovis Imperatoris”). At the same time, we translate 'Cesar' as 'Emperor' (so, for example, the Wikipedia entry see above).
Now, as an acclamation of victorious generals, the title 'Imperator' is already known since the 3rd century BCE and since Sulla (c. 138 BC – 78 BC), one began to count the number of times one received this title, a usage which was carried on beyond Cesar. Octavian/Augustus, for example, was acclamed 21 times 'Imperator', for the first time probably because of his victory in Brundisium he adopted the 'praenomen Imperatoris' (Inscr. Ital. XIII 1, see D. McFayden, The History of the Titel Imperator under the Roman Empire, Diss., [Chicago, 1920]), but only since Claudius (Emperor 41 to 54 AD), but already Julius Cesar was called imperator and for him this title was no longer simply a commemoration of a victory, but a title and expression of his absolute, dictatorial military power, was even used as part of his name: C. CAESARE IMP. (CIL 1².788). And when Cesar was murdered, Octavian not only was regarded as adopted by Cesar, but also chose as his name that of his 'father', became Gaius Julius Caesar, and later adopted his father's title Imperator Julius Caesar, as if imperator was a first name.This was made official by law in 29 BCE and could even be combined with the number of imperatorial acclamations, like CIL 5.526: IMP. CAESARI DIVI F. IMP. V). Two years later, Octavian settled for Imperator Caesar Augustus - three words that all became synonym of 'emperor' (see http://www.livius.org/).
Subsequently, Imperator became the second acclamation after the acclamation as Cesar - hence only from him onwards can we historically speak of a Roman 'Emperor'.
And yet, what do we mean by Roman Emperor? The main distinction is, of course, that he is no longer a representative of a Roman Republic, but the sole dictator in the Roman Empire. And in this respect, only Christian nomenclator stylised Augustus to being the 'romantic' Emperor known from the New Testament, not Cesar, although Cesar was not only the first dictator, but also passed on his name as a cognomen, a title and a political programme to his family and with Flavians beyond his family to all subsequent dictators of the Roman Empire and beyond.
