The word 'treehouse' and phrase 'tree house' are synonymous. The Oxford English Dictionary defines a tree house as: "A structure built in the branches of a tree for children to play in." The Treehouse Guide (this site) further defines a treehouse as: "A structure built in or around a tree which interacts with, and relies upon, the tree for its support. A treehouse consists of a roofed platform defining a sheltered space which may be fully enclosed for protection from the elements.