Frappe simply refers to a chilled drink that has been blended - it does not have to be made with coffee but it usually is.
Frappuccino® traditionally refers to when cappuccino, which is espresso mixed with foamed and steamed milk, is mixed with milkshake. Starbucks trademarked the name and now Frappuccino® is more like a milkshake that has been mixed with other flavorings. Frappuccino® will usually include coffee. However, there are a number of offerings now that do not contain any coffee - please see our Summer Coolers for ideas.