makes sense though.
just think of it this way. if you have two 12 volt lamps, if you want to run them off 12volts you run them in parallel if you want to run them of 24volts you run them in series.

on the williams/bally pins the transformer have 2 110v windings. if you want to run off 110v they are connected in parallel and if you want to run them on 220v (or 240v) they are connected in series.
this is done via the plug on the transformer.

but with gottlieb they have 2 transformers, both with 2 110v primary windings.  again If you need to run them off 220v to 240v you wire them in series. If you need to run them off 110v then you wire them in parallel