I found two IR diodes, not IR LEDs, but they look exactly the same and yet they yield different results. I found a circuit online for flame detection to try them out and they are definitely different diodes since the flame distance is different for both of them when it trips the LED in the circuit. How can I figure out the model number of the IR diodes with only the diodes?

 

You might find a drawing of the device that the diode came from. Other from that, hours of measuring the diodes and searching data sheets might work. A random part laying on your work bench might never be completely identified.