Can you please tell me what the difference between, dB and dBm when you are trying to test fiber optic cable.

Fiber optic power measurements are generally made in a log scale of "decibels" or "dB" (actually named after Alexander Graham Bell) that has a scale of 10 dB for every factor of 10 in power. The equation is actually:

dB=10 log (power 1/power 2)

dB is therefore a ratio measurement - 10 times more power is +10 dB and 100 times less is -20 dB, etc.
For ABSOLUTE measurements, you must have a reference point. If we use 1 milliwatt of power as our reference, our equation becomes

dB= 10 log (power/1 mW)

So now 1 mW is 0 dB, 10 mW is 10 dB, 0.1 mW is -10 dB, etc.