They are definitely two different species in my opinion. Here's what Mushroom Expert says on the subject:
"The separation of Pleurotus pulmonarius from the better-known, "true" oyster mushroom, Pleurotus ostreatus, is based on very good evidence that covers the three "species concepts" most commonly applied to fungi. In the laboratory, Pleurotus pulmonarius cannot "mate" with the other species in the oyster complex, so it is a good biological species. It also represents a fairly distinct morphological species, since it is paler (and frequently smaller) than the brownish Pleurotus ostreatus and appears to develop more of a stem, more of the time. DNA evidence supports Pleurotus pulmonarius as a phylogenetic species and, to top it all off, there is an ecological difference: it appears in warmer weather, appearing from late April through September, while Pleurotus ostreatus favors cold-weather conditions and appears from October through early April."