5v 10amp powering arduino and LED strip
My understanding is that the arduino and components plugged into the arduino will only draw as much amps as they need.


Your understanding is correct. You can go ahead with your plan.

I'm not sure what you mean when you say that connecting the Arduino to the power supply with an USB cable and connecting it with wires are two different options. Either way you're connecting the Arduino to the power supply.

You can read more details in this reference question here on Stack Exchange: Choosing power supply, how to get the voltage and current ratings?