An isolation transformer is a device that provides DC isolation from the power grid (or mains). At the same time, it provides an AC connection to couple in the power that you've connected to the grid...
The Scott-T transformer was used to run 2-phase equipment from a 3-phase source. Older power distribution systems (and equipment) were 2-phase.
An isolation transformer usually has the same input...
Isolation transformers are used to isolate one circuit from another. Highly sensitive circuits may require isolation from high power circuits, for example.