Transformers are rated as RMS, so the 16 V transformer is 16V RMS, however you measure it.
If you try to measure it with a scope you will see the positive and negative peaks greater than 22V and would need to calculate the RMS for yourself, unless the 'scope includes that function.
When rectified it will produce positive only peaks (i.e. DC) of around 22V, depending on the load and diode voltage drops. With no load the voltage will be highre due to the poor regulation from a transformer.
You need to add a suitably rated smoothing capacitor to "iron out" the peaks, see post #29.
For 12V DC you add a suitably rated (for the current you need) voltage regulator, following the data sheet for any other capacitors that may be needed.