What is an audio output transformer? Is it the same thing as an impedance matching transformer?
designed to operate at audio frequency or to match impedance?


Both. The specification of a transformer covers both its frequency range, and its turns ratio.

It gets more difficult to design a transformer as its frequency range increases.

The low frequency end is inductance limited, you need enough turns, and a high permeability core to increase the value of the primary inductance to something that doesn't shunt your signal too much.

The high frequency end needs few enough turns to keep the self-resonant frequency well above the top operating frequency, and the core needs thin laminations to keep the core losses down.

Once the core and basic number of turns has been established from the frequency range, then the turns ratio can be modified fairly freely to match impedances.

An audio output transformer matches the \$k\Omega\$ impedance of valve anodes to the single-figure \$\Omega\$ of loudspeakers, however there are many places where other ratios or even 1:1 are used for isolation.