When it comes to FELs, 'fastest' tends to refer to the length of the pulse, i.e. you're not interested in the speed at which the pulse propagates (which is obviously always $c$), but at how short an interval of time you can compress the energy into, as the pulse passes some pre-established target.
In general, free-electron lasers are able to produce some of the shortest pulses of light available, but they do tend to suffer somewhat from temporal jitter, which means that the pulses' length and timing are not as consistent as you would like. (That then means that the shortest available pulses of light, which also have a higher timing stability, are produced via high-harmonic generation, which strictly speaking isn't a laser, but a laser-driven parametric process.) The timing-jitter problem can be solved by providing the FEL with a 'seed': a low-energy pulse of light with a higher coherence and stability, that the FEL can then amplify. This can be done in one of two ways:
- one can use a pulse from an HHG source, which provides the best coherence properties, and which is currently only in use at the FERMI light source at the Elettra synchrotron in Trieste; or
- one can use a weaker FEL pulse as a seed, which the DESY team has been working on for some time and which they recently started reporting.
The news you heard refer to the opening of the European XFEL, which is an improved version of the seeded FLASH facility at DESY.
When it comes to the use of terms like "fastest", there's always a substantial amount of give in what does and doesn't count. As an example, single attosecond pulses produced via HHG can go below the 70 attosecond mark, much shorter and much more stable than seeded FELs (for comparison, the European XFEL specs claim pulses as short as 1 fs, though I would suspect there's significant timing jitter at that end of the range), but FEL people might want to dismiss them via technicalities ("they're not an actual laser") or on other figures of merit (FEL pulses are brighter) that make the comparisons that much more subjective. As such, it's normally safe to assume that when making those claims, the organization has bent some definitions so that they benefit them over their competitors.
Nevertheless, the sFLASH and European XFEL capabilities at DESY do represent a significant advance worth celebrating, and they do make us much more capable of producing short pulses (that are also useful in other aspects) than we were before them. That's what the 'fast' means in those news reports.