Both names are used for lots of different wetland plants. The original plant called a "reed" is Phragmites Australis. The original genus called a Bulrush is Typha spp. Phragmites ("reeds") carry their seeds apart from each other; Typha ("bulrush" or "cattail") carry their seeds in a tight bundle that looks like a spongy sausage. However, lots of plants that are not closely related to either Phragmites or Typha have been given the name "reed", "bulrush" or both. For instance, Papyrus is called both a reed and a bulrush in lots of old texts, but it's actually a sedge. Botany is confusing. If you're interested in starting to learn grasslike plants, remember: "sedges have edges, rushes are round, grasses have joints, and seagrasses drown"