Laser and CNC alignment

Does anyone know if the Laser module and CNC module have the same X and Y alignment for the laser and the CNC bit? I would hope this is the case.

In other words, if I put on the CNC module and drilled down at some X and Y coordinate, and then swapped to the laser module and with the laser engraved at that same X and Y coordinate, would the laser and cnc bit hit the same part of the material (just not sure since the X and Y coordinates define where the sliders are on the linear rails, not where the cnc bit tip/ laser hits, so if the laser module has the laser more to the left or right than the cnc module has the cnc bit, it may not hit the same spot).

Ideally if I use the CNC to cut an object out that I then want to engrave, it would be convenient to just switch out the laser tool head for the cnc tool head and keep everything else the same (same origin, same platform and mounting etc) and only need to adjust the Z axis origin for the laser

No they don’t.
My laser center is x=117.4, y=119.2 and the CNC is x=123.1, y=120.3

@Thick8
I wonder if thats consistent. If so maybe an easy way to get the same origin between CNC and Laser would be to Set the origin for CNC as the intended origin on the material, then when switching to the laser shifting the x over by 5.7 and the y over by 1.1. Do you think doing something like this could work?

Otherwise- is there an easy way (assuming I keep the material clamped on the platform in the same exact way) to make it so that the origin I set for the CNC and the origin I set for the laser end up hitting the same spot on the material?

Start with the CNC board. You will have the draw a (fine) line at the 125mm point of the y-axis between the lines at the 20 and 30 lines on the board on the 11 line of the x-axis. This will give you a cross mark at the center of the build plate. line up your laser with the center of the cross and write down the x,y positions. Do the same with the CNC and printer heads Write them on a small sticker or a piece of tape and stick them to the appropriate head.

That makes alot of sense. So in effect we are measuring how shifted the laser from cnc bit from 3d printing nozzel are when the tool heads are attached.

I likely wont always have my material perfectly centered, so I could probably draw a dot anywhere on the build platform and align the different tool heads with that dot and record all of the X and Y values. Then, if the laser lines up with it at X=3 and Y=5 and the CNC bit lines up with it at X=4 and Y=2 I know that to get the origin for the laser and the origin for the cnc to hit the same point (regardless of the where the point is) I need the cnc origin to be 1 to the right on the X and 3 down on the Y. Does that all make sense?