Gibson upright commercial freezer. I just replaced the capacitor and controller of which both burned up. I have a blue wire and white wire to connect to the controller. The controller has a L and N on it for the wires. What wire goes where? Can the compressor cause both of these parts to burn up? It was working fine up to the burnout.

Also, does it matter how the controller plugs to the three prongs on the compressor?

Are you saying it does not matter how the controller connects to the three prongs on the compressor?

And non-polar? You're saying the same thing? I find it interesting that the leads are labled L and N which I would guess means Line and Neutral??? But to confirm you are saying it does not matter where the blue and white wires go???

Thank you for your help!

This parts site shows a controller (start device) part AP2113685. The output, round pins plug right into the compressor pins.
Your old start device probably blew out on a power surge so your compressor is probably ok. Only way to know is to install the new controller. Best to use a 1000 joule surge protector in the outlet to prevent future problems. I use a Belkin 855 joule one available on Amazon, around $6.00.