I agree, Taxonomic confusion once again! I've always known these plants as Gaura, and Oenothera (Evening Primrose) as a different plant. I went ahead and added my photo's to the database at the Oenothera listing ... hope it's correct and doesn't cause a lot of work for the moderators.
The RHS site, shows Gaura lindheimeri with the common name of White Gaura. The ATP database has an Oenothera lindheimeri (with photo of a white bloom) with the synonym of Gaura lindheimeri.
The older I get, it doesn't take much to confuse me but I like to try to label my plants correctly ... getting harder and harder sometimes with so many changes.