I think the names attached to the end are probably slight variations of the same species Prunus cerasifera, they are still Prunus cerasifera. Nurseries selling them like to attach different descriptions.
What our database lists is "Prunus cerasifera var. pissardii" which is still Prunus cerasifera, not a synonym as such but some authority apparently thinks the 'var.' or variety name isn't significant.
The flowers on mine look like the photo taken at Kew gardens ..