Just wanted to add this for you to identify if your transformers are same type. View the labels on them. I took these out of my drawer to show the difference. Note that the low voltage end plug is same on both transformers.
12 Volts AC.
12 Volts DC.
Plugs are same, with insignificant difference of "STRAIGHT vs 90° "
12 Volts AC.
12 Volts DC.
Plugs are same, with insignificant difference of "STRAIGHT vs 90° "