Do I need both dry and liquid measuring cups?

Yes they're designed differently for accuracy. Dry measuring cups are meant to be filled to the brim and leveled off with a flat edge, giving you an exact measurement. Liquid measuring cups have extra space above the measurement line so liquid doesn't spill, and they're read at eye level at the meniscus (the bottom of the curved surface). Using a liquid cup for flour or a dry cup for milk leads to inaccurate measurements that can throw off recipes.