What are the two types of transformers?

The two general categories of transformer, based on their construction, are (a) mutual transformers and (b) autotransformers.

Mutual transformers have two coils, or 'windings', termed the primary (input side) and the secondary (output side), which are electrically isolated from each other, being linked with a magnetic field.

Autotransformers have a single, shared, winding and so, do not provide isolation between the primary and secondary sides.

Mutual transformers can be further classified, according to their function: e.g. power transformers, distribution transformers, isolation transformers, instrument transformers, matching transformers, etc.