You didn't mention what part, so I'll provide a random example:
http://www.murata-ps.com/data/magnetics/kmp_5100.pdfThe 51505C shows common mode starting to drop at 1kHz, peaking to -50dB just below 400kHz, then rising more or less from there (possibly with an antiresonance at 20-30MHz... which is pretty crappy of them, since most customers will be interested in the 0.15-30MHz range -- marketing shame, anyone?). Common mode is tested with both windings in parallel, connecting a 50 ohm signal generator in series with the choke, to a 50 ohm terminated load, which senses the attenuation.
Differential is tested with inverse signals applied to each winding, 50 ohm terminated. The total impedance as seen by the choke is therefore 100 ohms. The input and output voltages are sensed differentially. The 51505C starts dropping off around 1MHz, hits a peak at 8MHz and rises from there (probably hitting numerous resonances and anti-resonances in the 20-100+ MHz range).
Note that the resonances aren't even in the same place, so you can't guess, based on common mode response, what the differential response may be.
You may also see "normal mode", which is either synonymous with differential, or measured with one winding shorted (roughly equivalent, but won't be exactly the same around the higher resonances), or one winding alone (the other(s) open circuit). Hopefully, they provide a definition.
If you see a choke listed by impedance rather than attenuation, the difference is simply the attenuation as an impedance divider in the system impedance (50 ohms or so).
Measurements are similar for ready-made filter modules, except that it's always by attenuation, and the measurements are always relative to chassis ground (leaving three modes: common, differential, and single line).
Tim