If your meter is meassuring RMS AC sine wave voltage,,,,,,,the Transformer has a 5 to 1 turns ratio (its a 120 to 24 transformer) ,,,,,,,,,,the meter reads 120 VAC in, Id expect the same meter to read 24 VAC out unloaded,,,,,,,,,,Even if loaded and within the power and amperage rating of the transformer, Id still expect to see that same 5 to 1 ratio of AC voltage difference......As Bob correctly notes, once the output is full or half wave rectified youre NOT gonna get the same voltage reading, the above figures ar for the AC to AC transformation and RMS values..... You cant compare apples to oranges,,,,,,theres AC RMS and theres straight pure DC and theres half wave or full wave rippled DC and theres filtered DC.....
John T Too long retired EE and rusty on this so no warranty, Im better at AC Distribution or tractor DC stuff