We may have moved past this, but I've never heard of ginger soda before in any context. I would say I had a 'soda' when I've had a ginger ale but I wouldn't say ginger soda. And the only thing I know about ginger beer vs ale is that ginger beer is spicier from the ginger level. Ginger is pretty darn gross when there's too much like I've tried ginger shots before and it's an absolutely horrible, 'spicy' flavor in that quantity.
This is exactly what prompted my confusion originally. I'd never heard of ginger soda other than calling a ginger ale a soda but apparently Vernor's actually labels theirs as "ginger soda"