Past X-ray observations of the nearby luminous quasar PDS 456 (at z = 0.184) have revealed a wide-angle accretion disk wind with an outflow velocity of ∼−0.25c, as observed through observations of its blueshifted iron K-shell absorption line profile. Here we present three new XMM-Newton observations of PDS 456: one in 2018 September where the quasar was bright and featureless and two in 2019 September, 22 days apart, occurring when the quasar was five times fainter and where strong blueshifted lines from the wind were present. During the second 2019 September observation, three broad ( = 3000 km s−1) absorption lines were resolved in the high-resolution Reflection Grating Spectrometer spectrum that are identified with blueshifted O viii Ly , Ne ix He , and Ne x Ly . The outflow velocity of this soft X-ray absorber was found to be v/c = −0.258 0.003, fully consistent with an iron K absorber with v/c = −0.261 0.007. The ionization parameter and column density of the soft X-ray component (log = 3.4, NH = 2 × 1021 cm−2) outflow was lower by about 2 orders of magnitude when compared to the high-ionization wind at iron K (log = 5, NH = 7 × 1023 cm−2). Substantial variability was seen in the soft X-ray absorber between the 2019 observations, declining from NH = 1023 to 1021 cm−2 over 20 days, while the iron K component was remarkably stable. We conclude that the soft X-ray wind may originate from an inhomogeneous wind streamline passing across the line of sight that, due to its lower ionization, is located further from the black hole, on parsec scales, than the innermost disk wind.