Tornadoes and twisters are the same thing. Hurricanes and typhoons are also the same (hurricanes occur in the Atlantic and Eastern Pacific, typhoons occur in the Western Pacific). The term 'cyclone' is more ambiguous. Some people, especially in the US Midwest and Plains states, call tornadoes cyclones. However, the true definition of cyclone is 'an area of closed, circular fluid motion that is rotating in the same direction as the Earth'. So hurricanes and typhoons are very large cyclones, while tornadoes/twisters are much smaller cyclones.