Does amperage matter with a solar panel?

I understand that voltage matters when connecting a solar panel to a solar controller. I think of voltage similarly to when you plug something into AC mains such as that you will destroy something designed for 120 volts if you plug into a 240 outlet.

I think I understand wattage as well, if I am correct, if I plug in a 10-watt LED light into a 20-amp circuit, the LED will only draw what it needs, 10 watts.

I do not understand how amperage affects solar panels? Does it matter if a panel produces more amperage than a solar controller is rated for?