Cooking terms in other languages can be confusing, especially when they sound alike but describe two very separate things. For example, strudel and streusel sound very similar -- and are both baking terms -- but have no direct relationship, despite that linguistic resemblance.
Streusel is the sweet, golden crumb-like topping you frequently see baked onto the tops of muffins, coffee cakes, pies and other baked goods. The simplest versions consist of just sugar and butter mixed with flour. Add a pinch of salt or warm spices to enhance the sweet flavor, and then scatter crushed nuts or fine oatmeal for texture. Sprinkle the mixture over your baked goods before they go into the oven, so the crumbs of streusel topping can meld with the batter as it bakes. Streusel-topped goods will lose their sweet sprinkles if they're turned out of their pan onto a cooling rack, so use paper liners or pans with removable sides whenever possible.
Streusel isn't restricted completely to use as a topping. Shoo-fly pie, an Amish classic, is made by thickening a molasses-based filling with streusel-style crumbs.
Strudels are a souvenir of the Ottoman Empire's 17th-century invasion of Europe, which came as far as the gates of Vienna, Austria. The Turks brought with them a range of sweet and savory pastries wrapped in crisp yufka dough, their version of phyllo. The nations of Central Europe quickly adapted these pastries, making them their own.
A traditional strudel is made by rolling and stretching a very thin sheet of dough until it's all but transparent, then brushing it with melted butter. It's filled with fruit or savory fillings, rolled and baked to create multiple thin, crisp layers. The name strudel, which means "vortex" or "whirlpool," comes from this rolling process.
Making the dough from scratch is a time-consuming process, so bakers often substitute sheets of store-bought phyllo pastry. When brushed with melted butter and layered together, the sheets of phyllo make a strudel that closely resembles one made with homemade dough. They're smaller than a traditional strudel, which uses a table-sized sheet of dough, but the sheets can be overlapped as needed to create larger pastries.
Assembling layers of phyllo pastry is easier than making strudel dough from scratch, but it's still time-consuming. An alternative technique, used in Germany and elsewhere, is to use puff pastry for the crust. Puff pastry is crisp and flaky, like phyllo, but provides hundreds of layers in a single, easy-to-use sheet. Sealing a fruit or savory filling inside a folded sheet of puff pastry takes just seconds, and bakes to a beautifully golden finish.