This basically says that all actions that involve leaving the place you live, can be called 旅行. Eg. I'm going on a business trip to Shanghai; I'm going to the Nasdaq to take part in their IPO - both of these can be called 旅行. Only when you go to a place and travel around the area, can you use the word 旅遊. Eg., At the weekend I'm driving to Baihua Shan (to go sightseeing); I'm going to Saipan on holiday - both of these are 旅遊. The national tourist bureau is called the 旅遊局 and can't be called the 旅行局.
環遊 only every appears in the phrase "環遊世界", which means to go travel the World.