I have been doing a lot of research online about it, and it seem pretty confusing. I could be wrong on this, but it seems like "fast" bass is bass music with a lot of transients, quick transitions from one bass note to another. In other words, a subwoofer that plays "fast bass" well, is the one that has good transient response. And transient response is defined roughly how fast a speaker will respond to sudden one time impulses, which includes the complete time domain response to such an impulse, which includes, both the start time and end time. Based on this, a "fast" subwoofer should basically play more refined bass, with sharp, well defined edges between notes, while the "slow" subwoofer will sound a little more "washed out", even when it may have a perfectly good frequency response in the considered frequency range. There does not seem a good coherent agreement on whether which specs will suggest that a subwoofer has good transient response. Box size seems important. Inductance seems important. There is also some evidence that larger diameter cones seem to have a slower decay time in their transient response, so big vs small subwoofers and fast bass is not completely a myth. Finally, box alignment is important. Subwoofers Q (usually computed by box modeling software) depends on box size, and Q of 0.707 or lower is considered best for transient response (essentially bigger box), but such Q alignment may reduce power handling at lower frequencies.
If you want to waste a couple of hours of your time, find the "fast vs slow bass" threads on
DIYMA. There is a lot of noise there, but some posts are interesting.