I can see that the "-" pins are tied together (from the photo), so, how about using an Ohmmeter (or continuity tester) to check if the two pins, both marked "PWM/TTL" are connected together, and thus are the exact same connection.
If so, then it's a fair bet that connecting the Arduino Gnd to the "-" pin on your Laser, and the "PWM/TTL" pin to one of the PWM outs on the Arduino, is the correct way to go.
Also, here's a couple of links I found that discuss this very thing:
- Talk Manufacturing | Hubs
-
https://www.machsupport.com/forum/index.php?topic=30369.0
And I found these specs on a 15W Laser board that looks similar to yours ("open" is probably a mistranslation for "on", like the "Valve is open":
- Modulation frequency: ttl can be modulated
0v- Off
5v open
Pwm frequency <9Khz
And, as for how to connect this along with the CNC Shield -- are there any Arduino pins not being used by the Shield? Is there a diagram for that Shield available? Looking at traces might not be enough, as there is the possibility of more than 2 layers. Beyond that, perhaps your answer is in one of the above links or maybe someone else has more experience with this.