A transformer sold for isolation is often built with special insulation between primary and secondary, and is specified to withstand a high voltage between windings.
Isolation transformers with electrostatic shields are used for power supplies for sensitive equipment such as computers, medical devices, or laboratory instruments.
A grounded Faraday shield between the primary and the secondary greatly reduces the coupling of common-mode noise.
Differential noise can magnetically couple from the primary to the secondary of an isolation transformer, and must be filtered out if a problem occurs.
An example is the Austin transformer for the power supply of air-traffic obstacle warning lamps on radio antenna masts.
Without the isolation transformer, the lighting circuits on the mast would conduct radio-frequency energy to ground through the power supply.