Both wigglers and undulators use periodic magnetic fields applied to stored relativistic electron beams to produce intense beams of UV or X-rays that can be used in a wide range of condensed matter physics and materials science experiments.
This helpful answer to a different question states:
As for the difference between undulators and wigglers: synchrotron radiation has a characteristic opening angle (that goes as $1/\gamma$). In an undulator, the electron motion in the transverse direction is set to be on the order of the opening angle. In a wiggler, however, the motion is made to be larger than the opening angle and therefore a wider beam results.
That answer also links to a google books webpage for Synchrotron Radiation Sources: A Primer which says in section 14.2.2 (undulator radiation):
In an undulator, radiation from the various periods interfere coherently. Sharp peaks are produced at harmonics of the resonant frequency, which depends on the electron energy, the undulation period and field strength, and the observation position. The optical wavelength is a Lorentz transformation of the undulation period into the beam frame followed by a relativistic Doppler shift back into the laboratory frame. The velocity used in the Lorentz transformation and the Doppler shift is the longitudinal electron velocity, which is less than the full electron velocity because of the electron’s curved path through the undulator.
Functionally speaking, it sounds like a wiggler could be characterized as an incoherent, underperforming undulator.
An undulator used with the wrong electron beam energy would be in effect a wiggler.
The narrow energy spectrum from a properly operated undulator, the result of the coherent addition in the forward direction would spread out to a broadband spectrum several orders of magnitude wider in energy and lower in brightness (energy per unit energy and solid angle) when operated with the wrong electron energy or the wrong alternating magnetic field strength.
Am I missing something fundamental, or does this pretty much describe the difference between the two devices?
note: I'm not asking for the difference between the two beams, I'm asking about the devices themselves, so if there are specific issues with their magnetic field designs that would be more interesting than differences in beam characteristics.