That’s just a confusion over terminology – it is one and the same thing.
35mm slides refers to the photographic film format (the images are exposed on a roll of film that is 35mm wide, the actual visible area being 36mm x 24mm).
50mm (actually 50mm x 50mm) refers to the overall size of the mount that contains the photographic film. In the ‘old days’ we referred to “two by two” slides, meaning 2 inches x 2 inches (50xmm x 50mm).
50mm square slide mounts fit all slide projector magazines designed for the 35mm film format. There is however a complication over the thickness of the mount – our glass slides are 3mm thick and fit all Kodak Carousel slide projectors but may not fit other brands of projector. Our glassless slides are 2mm thick and will fit all slide magazine produced over the last fifty years.