Is my Anchor Hocking Oven Basics glass measuring cup inaccurate?
I'd get a third measuring tool to see which one is wrong.

One way to test this is to measure by weight (and IMO, all recipes should list ingredients by weight instead of volume)

1 cup of water is about 236ml which is 236g.

Get 1 cup from your red cup and weight it.
Get 1 cup from your glass cup and weight it.

It should tell you which one is right.

And to answer your question, yes, for some recipes, if you add too much or too liltle liquid it will not result in different results (either too dry or too wet).