I purchased my first Lego train set (for my son's really

and the AC transformer is burned out. It is a 12VAC 7VA unit. But searching around for other train stuff it always mentions 9 Volt sets, but those sets appear to be the same as mine. I am confused. Is this 12V set an anomoly ? If I purchase another set like this Harry Potter one on sale at Costco, will it run at 12V ?
Some clarification on these different kinds of voltages would be appreciated. Also, the name of a good place to get a replacement AC adapter would be appreciated. I know I can purchase an adapter/controller set at the Lego store but I'd prefer to spend less money.
Thank you,
Terry.