Yes in measuring terms the 1 cup dry is the same as 1 cup liquid.
Whether the cup has liquid or dry they are the same amount of volume and take up the same space.
So you can use any 1 cup measuring cup to add 1 cup of liquid or 1 cup of powdered or dry ingredients to the recipe that you're making.
If you fill one cup full of liquid and then measure 1 cup of dry ingredients and then fill the same cup it will turn out the same.
Because both dry ingredients and liquid take up the same exact amount of space in the one cup measuring cup.
So yes 1 cup of dry ingredients equals the same as 1 cup liquid ingredients.