Saber-toothed cats were not tigers. They were a family of extinct cats called Machairodontinae. These cats were diverse, with many different species, and they lived across various parts of the world.
Since they were extinct, there is no specific name for an adult saber-toothed cat. They were simply referred to as adult saber-toothed cats or by their species name, such as Smilodon fatalis (the most famous species).