If I say "he traveled around the world", I usually mean that either he travelled to a place on the opposite side of the world (like Australia), or else he circumnavigated the world in a single trip like Magellan. If I say "he has traveled all around the world," it means that he has traveled to several different parts of the world at several different times. Since you want to show that English is spoken in several locations on the globe, use "all around."

They can mean the same thing