Most of the dragons in the films seem to be based on the modern design rather than the classic design for dragons; most noticeably, their wings don´t sprout from their back, but are rather the modified forelegs of the dragon (as in real life bats and flying reptiles or pterosaurs). This style of dragon is actually known as the "Wyvern". Apparently in the movieverse, dragons and wyverns are one and the same, although wyverns are more commonly used than four-legged dragons.
Most of the dragons in the films seem to be based on the modern design rather than the classic design for dragons; most noticeably, their wings don´t sprout from their back, but are rather the modified forelegs of the dragon (as in real life bats and flying reptiles or pterosaurs). This style of dragon is actually known as the "Wyvern". Apparently in the movieverse, dragons and wyverns are one and the same, although wyverns are more commonly used than four-legged dragons.
http://harrypotter.wikia.com/wiki/Dragon