'Tartaria', 'Tartary', 'Tatary' and all their derivatives refer to an ill-defined geographical space, typically encompassing Central Asia (the '-stans') and Inner Asia (East Turkestan and Mongolia, often extended to include Tibet and Manchuria), largely but not entirely inhabited by the descendants of the Mongolic and Turkic peoples of the former Mongol Empire. As /u/kochevnik81 notes in this answer (which I highly suggest you read), there was no united state of 'Tartary', but rather a range of successor khanates and hybrid states like the Chagatai Khanate, the Emirate of Bukhara, and the Khanate of Kazan. Latterly, from the mid-16th century onward, 'Tartary' would come to be divided between two states: Muscovy-Russia, approaching from the west, and the Manchu Qing, approaching from the east. Consequently, later maps showing 'Tartary' distinguish between 'Independent Tartary' (latterly 'Russian Tartary') and 'Chinese Tartary'.
Now, if it seems like 'Tartary' was the largest empire to have ever existed, that's because in one sense it was... because 'Tartary' refers in large part to the geographical scope of the former Mongol empire, albeit excluding its settled conquests in China, Iran and Eastern Europe. There's a lot of pseudo-historical stuff out there about the existence of some unified 'Tartar' state in the late Medieval and Early Modern periods, but that's all based on misreading geographical terms and taking Western European ignorance about Inner Asian geography as actual fact. Again, I urge you to read through Kochevnik's answer, linked above.