Are AC adapters electrically isolated?
You mix up "isolated transformer" with "isolation transformer". The latter is a transformer that has only one single goal and that is galvanic isolation from the mains supply, without changing the voltage. These transformers are often used for testing, so it is somewhat safer to accidentally touching one of the conductors.

All normal transformers, when properly connected, offer galvanic isolation, but beware that there do exist types (like autotransformers) that are internally wired in such a way that they don't. When unsure measure resistance between primary and secondary windings, this should be very high.