there are THREE(3) possible voltages.
#1)
the Arduino requires a voltage.
#2)
the COIL, and only the coil of the relay, just the coil itself, requires a very specific voltage and that is printed on the case of the relay or in the model number or on the manufactures data sheet.
#3)
the CONTACTS... well, these are just wires, so you pick whatever you want as long as the wires can handle the power.
we have to add things to make it do what we want. in some cases, we add a diode, sometimes it is already installed, some times, we do not care because the relay board is isolated from the Arduino.
sometimes the relay is put on a board for us and sold as a unit. the manufacturer might add things like opto-isolators, or transistors or other things, and then tell us that they only need 5v and 10mA. this is common with the board you have.
this is the part you seem to be having a hard time grasping.
all the ARDUINO does is to change the state of the opto-isolator. an opto-isolator is like an LED inside of a box. you light that LED and inside that tiny box, there is a receiver that sees that LED and then it does whatever it does.
the connection between your device and the other side is light. only light. since it is light, we call that optical, or opto for short. and because there is no electrical connection we call that isolation so we call this an opto-isolator.
someone else picked all the electronical bits on the other side of that opto-isolator, so you do not have to.
but, you have to apply power that the COIL requires. when they made that circuit, they picked everything needed to work with that voltage.
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