Can I use a PET capacitor in a power supply? What's the difference?
The main things that you need to look at when selecting capacitors for a power supply is the voltage rating of the capacitor, if it needs to be polarized, and the equivalent series resistance.

The datasheet of the IC that you are using will specify what value of capacitor you need and many times will specify the actual type of capacitor required.

Electrolytic Caps are polarized which doesn't work well for AC signal, but is the cheapest way to get a high value capacitance, which is why they are used a lot in power supplies.

So, in short, yes, any cap should work OK as long as you are in the allowable voltage range.