SSR (for your application the 10A model should be fine).
It has two input pins that accept dc 3V to 24V (sometimes 36V) . There is +v screw term and a GND screw term.
For simple on/off , a digital HIGH connected to these two pins turns on the SSR.
The SSR output screw terminals should be treated exactly like relay spst contacts. Cut the LINE (HOT) connect one of the cut wires to one of the OUTPUT screw terminals and the other cut wire to the other screw terminal.
For duty cycle (variable )control of the SSR , use a PWM pin & GND to control the dc input screw terminals intead of a digital pin.
If you use one of the PWM pins then you can do either.