Emperor
The first Austrian Emperor was the last Holy Roman Emperor Francis II. In the face of aggressions by Napoleon, Francis feared for the future of the Holy Roman Empire. He wished to maintain his and his family's Imperial status in the event that the Holy Roman Empire should be dissolved, as it indeed was in 1806 when an Austrian-led army suffered a humiliating defeat at the Battle of Austerlitz. After which, the victorious Napoleon proceeded to dismantle the old "Reich" by severing a good portion from the empire and turning it into a separate Confederation of the Rhine. With the size of his imperial realm significantly reduced, Francis II, "Holy Roman Emperor" became Francis I, "Emperor of Austria". The new imperial title may have sounded less prestigious than the old one, but Francis' dynasty continued to rule from Austria and a Habsburg monarch was still an emperor ("Kaiser"), and not just merely a king ("König"), in name.
Emperor
From the time of Otto the Great onward, much of the former Carolingian kingdom of Eastern Francia became the Holy Roman Empire. The prince-electors elected one of their peers as King of the Romans and King of Italy before being crowned by the Pope. The Emperor could also pursue the election of his heir (usually a son) as King, who would then succeed him after his death. This junior King then bore the title of Roman King (King of the Romans). Although technically already ruling, after the election he would be crowned as emperor by the Pope. The last emperor to be crowned by the pope was Charles V; all emperors after him were technically "emperors-elect", but were universally referred to as "Emperor".