24V PIR

I have a PIR shown in an image below. Its powered by an external 24v DC power supply and seems to operate an internal relay.

I know little about these but it has three connections, a live(Blue), ground(Brown) and output (Red).

Using a multimeter with the prongs connected to live and the output I can see that when the PIR is triggered the relay will create a circuit between the live and output pushing out 24v.

I am I correct in assuming that this kind of PIR cannot be used with an Arduino since it would need to be powered by an external PSU? Apart from the obvious different in voltage, I would assume that without a ground from the Arduino and a 3.3v signal being fed back from the output into an input that a complete circuit could not be made?

Not everything is black and white.

Is relay closure between red and brown. If so the the step up should work satisfactory. Just watch isolation of 24 supply from output closure since they share common ground.
If relay is switching blue to red then you will need to take more step then just raising voltage.
The 115 volt models of these drop the 115V to 24V then drop the 24V to 5V ot operate all but the relay.
So if you have a schematic for the PIR you may find a bit of modification will make it all 5V

The relay will close between the red and blue.

I would prefer to power the pir from an external source if possible, I am looking at, at least a 5 meter run of the PIR from the arduino, my particular model is micro sized and only has 3.3v available, I am worried about the voltage drop at that voltage and distance.

The first option provided looks good, but I would rather purchase a pir off the shelf which would run either on main's AC and/or 12/24v dc but with a 3.3v output.

Since I don't think I can share the same ground are there any PIR's out there that will have a separate 3.3v and ground output? I.E four total pins, +/- Power, +/- sensor. Would that be the best way to go, or am I totally confused?

Cooper Lighting Model MS180W is a 115V versions. It runs on 115 and the relay provides 115V on detect.

With this I power a separate relay (115V) and take the relay contacts to Arduino. Using ground and input pin with a pullup resistor.