Transformer, Power supply, Switching, Adapter... Whats the difference?

Hello All, Newbie here. I know its probably a dumb question but whats the difference? I need a Condor desk top transformer 12v DC 3.3A for a neon sign. the one I am replacing has coils around iron??? looks heavy duty and I am afraid to replace it with some wimpy wall wart. As you can tell I know little about electronics but love to tinker with it. Also the condor transformer say input 120V 60Hz 60W. What does the watts relate to. The higher the Watts the heavier duty it is??? I thought neon needed high voltage.
Thanks
Would this one work?
**broken link removed**

Switching????What?

The "coils around iron" is the transformer.

"Wattage" (i.e. "Watts") is the unit of measurement for "power", and power is the product of voltage and current (Power = Voltage x Current, or P = I x E). It tells you how much current it can source at its rated secondary output voltage as well as how much current it will draw at its rated input voltage.

As to the switching power supply (better known as a Switch Mode Power Supply or SMPS), it takes the line voltage, converts it to DC, then "switches" it on and off at a frequency much higher than the wall voltage. It then feeds this new high frequency square wave AC into the unit's power transformer. With high frequency AC power, you're able to get the same power out of a much smaller power transformer, which allows them to downsize the supply while maintaining its power delivery capabilities.