Why is the Ottoman Empire called an empire? Why not just call it the Ottoman Sultanate?

Because it was only a ‘sultanate’ from the time of Orhan (r. 1323–62) to that of Mehmet Fatih (r. 1444–46, 1451–81), and the latter’s conquest of Constantinople. After that, he was titled as ‘Padishah’ - master of kings - and all members of the ruling family (men and women) bore the title of sultan, analogous to the Habsburg style of Archduke for all members of their house. ‘Sultan’ was just the commonly used appellation in English; the Spaniards used ‘Grand Seigneur’ - Great Lord - while the Indo-Iranian world used ‘Kaiser’ - Caesar. In the 19th century, Ottoman diplomats were scrupulous in seeing that padishah was always translated as emperor in foreign correspondence, never as sultan or king.

More properly, the Ottoman state never defined itself as an ‘empire’ on the same terms as the Roman one that had preceded it, though the Ottoman sovereign did claim the Roman imperial dignity as one of his titles. The correct term would be ‘Devlet-i Aliye’, usually translated as Sublime State, but more literally meaning Sublime Era or Cycle of time; this was the same terminology used by the other great Persianate states of the age (Iran and India). The raison d’etre of the state was to maintain the nizam-i alem, the natural ‘order of the world’ equally between people and social classes as between religious communities and political entities. This is quite appropriately untranslatable; empire would indeed once have been the proper word, in that the medieval ‘Romanesque’ conception of the Empire (in the singular, Roman, Christianate sense) was very similar, but is entirely unlike modern ideas of empire as a multi-ethnic state (which ideas owe their existence to Anglo-Saxon fears of decadent Catholic Europe vs. clean, national little England). To find the real modern translation we would need to dig into the American, Soviet & Chinese languages of exceptionalism, and borrow a terminology modern people would be loath to apply to anybody but themselves.

It is worth noting that by the 14–15th centuries, the era in which ‘Sultan’ or ‘Sultanate’ could potentially denote a powerful ruler or a great state was swiftly passing away. In the 10th and 11th centuries, when the title was first used by the world-spanning Ghaznavi and Saljuq dynasties that was indeed the case. Sultan (authority) was meant as a more strongly-worded version of ‘amir (governor) of a province of the caliphate, in that a sultan claimed autonomy and was not selected by the caliph (regent) at Baghdad, although he did seek the latter’s permission and appointment.

By the 14th century, although the title was still in use by the Mamluk sultans of Egypt (who had a pet caliph as a pensioner at their court, and so could afford to play humble and old-fashioned with their titulature, insofar as their state still effectively claimed the highest sovereignty and had no external caliph to tell them otherwise), it was already a minor one. In later centuries, the only people who claimed the sultanic authority as their highest were petty rulers whose authority centred on a single city, not a nation. The only sovereign modern sultanate, Oman, is of this sort - the ‘Sultan’ was originally the sultan of Musqat, the most important local trade city, and only with British help did he secure a kingdom for his dynasty (the country, or Oman proper, was ruled by an elected Imam).