PSR J1814-1744 is a 4 s radio pulsar with surface dipole magnetic field strength 5.5 × 10¹³ G, inferred assuming simple magnetic dipole braking. This pulsar's spin parameters are very similar to those of anomalous X-ray pulsars (AXPs), suggesting that this may be a transition object between the radio pulsar and AXP population, if AXPs are isolated, high magnetic field neutron stars as has recently been hypothesized. We present archival X-ray observations of PSR J1814-1744 made with ROSAT and ASCA. X-ray emission is not detected from the position of the radio pulsar. The derived upper flux limit implies an X-ray luminosity significantly smaller than those of all known AXPs. This conclusion is insensitive to the possibility that X-ray emission from PSR J1814-1744 is beamed or that it undergoes modest variability. When interpreted in the context of the magnetar mechanism, these results argue that X-ray emission from AXPs must depend on more than merely the inferred surface magnetic field strength. This suggests distinct evolutionary paths for radio pulsars and AXPs, despite their proximity in period-period derivative phase space.