Unregulated AC-DC adaptor voltage response
If it doesn't contain a voltage regulator then it's going to be a little difficult to predict the voltage but, what can be fairly certain is that if 800mA were being taken from the terminals then the terminal voltage is going to be 12V with maybe a +/-1 volt tolerance.

It possibly contains a regular AC step-down transformer that might have a line regulation of 20% - this means when no-load is being taken, the terminal AC voltage on the secondary is 20% high. Add this to 12 volts and you get 14.4 volts DC.

Maybe you can also say that on no-load the bridge rectifier diodes will have a forward volt-drop of 0.4 volts and that on full load they are 1.0V. There are always two in circuit so that could account for another 1.2 volts bringing the teminal voltage off-load up to 16 volts.

What about ripple - if it is an unregulated supply then on-load there will be significantly more ripple voltage than on no-load (almost no ripple voltage). You could say that if the ripple voltage (on load) was 4Vp-p diminishing to 0Vp-p (off-load), the average voltage output voltage will be 50% of the ripple p-p voltage lower on full-load than no-load i.e. this accounts for another 2 volts.

This might bring the grand total up to 18 volts off-load and 12 volts on load.

Speculation on my part but not a million miles off.