Decibel (dB) and dB relative to a milliwatt (dBm) represent two different but related concepts.
A dB is a shorthand way to express the ratio of two values. As a unit for the strength of a signal, dB expresses the ratio between two power levels. To be exact, dB = log (P1/P2).
Using the decibel allows us to contrast greatly differing power levels (a common predicament in radio link design) with a simple two- or three-digit number instead of a more burdensome nine- or 10-digit one.
For instance, instead of characterizing the difference in two power levels as 1,000,000,000 to 1, it's much simpler to use the decibel representation as 10*log (1,000,000,000/1), or 90 dB. The same goes for very small numbers: The ratio of 0.000000001 to 1 can be characterized as -90 dB. This makes keeping track of signal levels much simpler.
The unit dBm denotes an absolute power level measured in decibels and referenced to 1 milliwatt (mW). To convert from absolute power "P" (in watts) to dBm, use the formula dBm = 10*log (P/1 mW). This equation looks almost the same as that for the dB. However, now the power level "P" has been referenced to 1 mW. It turns out that in the practical radio world, 1 mW is a convenient reference point from which to measure power.
Use dB when expressing the ratio between two power values. Use dBm when expressing an absolute value of power.