a double hatrick is 4 wickets in 4 balls but it should not be.
While the logical sequence is wickets 1,2,3 and 2,3,4 the reality is that this shouldn't be considered a double hat-trick as wickets 2 and 3 are not unique in both sequences. Just because something is very unlikely (i.e. six in a row) doesn't mean that giving something the wrong name is correct. The reality is that with this measure, a centruy is 100 runs and a double is 101 runs, which no-one will agree with, but that's because double centuries occur more commonly than six wickets.
It seems to be a term that is pretty much entirely a Southern Hemisphere one, coined because you need to call 4 in a row something, however incorrect that may be... A true double, whether it is a hat-trick or century, is six wickets or 200 runs, each of which is unique.