You got it right although the taps from the transformer give different volt outputs, up to 30V (Vp much higher) and the meters ware for AC. I wouldn't trust it
That is no load voltage and it does not mean nothing because secundary voltage is limited by the battery.
Transformers for battery chargers have a high short circuit voltage (above 20%) to limit charging current.
NB: short circuit voltage is how much % of nominal voltage you have to apply to the primary to obtain the nominal current with the short circuited secundary.
In normal working, you switch the taps to ajust the charging current.
AC voltmeter (moving iron) may also measure DC voltage.
What you should look for is if it measuring voltage before or after the rectifier.