  We analyze a 7.4 hr XMM-Newton light curve of the cataclysmic variable Swift
J0503.7-2819, previously classified using optical periods as an intermediate
polar (IP) with an orbital period of 0.0567 days. A photometric signal at 975
s, previously suggested to be the spin period, is not present in X-rays and is
readily understood as a quasi-periodic oscillation. The X-ray light curve
instead shows clear behavior of a highly asynchronous polar (AP) or stream-fed
IP. It can be described by either of two scenarios: one which switches between
one-pole and two-pole accretion, and another in which accretion alternates
fully between two poles. The spin periods in these two models are 0.0455 days
and 0.0505 days, respectively. The spin frequency $\omega$ is thus either 24%
faster or 12% faster than the orbital frequency $\Omega$, and the corresponding
beat period between spin and orbit is 0.231 days or 0.462 days. Brief
absorption events seen in light curve are spaced in a way that may favor the
longer spin and beat periods. These periods are confirmed and refined using
data from the Transiting Exoplanet Survey Satellite (TESS) and the Asteroid
Terrestrial-impact Last Alert System (ATLAS). The short beat cycle of Swift
J0503.7-2819 makes it well-suited to resolving this common dilemma, which
amounts to deciding whether the main signal in the power spectrum is $\omega$
or $2\omega-\Omega$.
